The required answer is the value of tan(2) is approximately -2352/3669.
To evaluate the expression under the given conditions, we will first determine the value of sin() using the Pythagorean identity and then use the double-angle formula for tan(2).
A Quadrant is circular sector of equal one quarter of a circle ,or a half semicircle. A sector of two-dimensional cartesian coordinate system. The Pythagorean identity, are useful expression involving the function need to simplified.
Given: cos() = 7/25, and is in Quadrant I.
Step 1: Find sin()
Since we are in Quadrant I, sin() is positive. Using the Pythagorean identity, sin^2() + cos^2() = 1, we can find sin().
sin^2() + (7/25)^2 = 1
sin^2() = 1 - (49/625)
sin^2() = (576/625)
sin() = √(576/625) = 24/25
we are called the Pythagorean identity is Pythagorean trigonometric identity, is expression A to B .
The same value for all variables within certain range. Angle is double or multiply by 2 so we called double- angle.
Step 2: Find tan(2) using the double-angle formula
The double-angle formula for tangent is: tan(2) = (2 * tan()) / (1 - tan^2())
First, we find tan():
tan() = sin() / cos() = (24/25) / (7/25) = 24/7
Now, use the formula for tan(2):
tan(2) = (2 * (24/7)) / (1 - (24/7)^2)
tan(2) = (48/7) / (1 - 576/49)
tan(2) = (48/7) / ((49 - 576) / 49)
tan(2) = (48/7) * (49 / (-527))
tan(2) = (-2352 / 3669)
So, under the given conditions, the value of tan(2) is approximately -2352/3669.
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Which of the following tables represents a linear relationship that is also proportional? x y 0 3 3 6 6 9 x y 0 4 2 6 4 8 x y 0 0 6 3 12 6 x y 0 3 5 5 10 7
Choice B, with a y-intercept of 0, is the correct response and provides a table that depicts a linear and proportionate relationship that is
x y
0 0
2 1
4 2
What do you mean By graph Intercept function?
The graph's intercept is the location where the line or curve crosses the axis. The term "x-intercept" refers to a point that crosses the x-axis. The y-intercept is the location where a point crosses the y-axis. Here is a y-intercept illustration. Suppose the line y = x+ 3 exists. This graph's y-axis intersects at this location (0,3). So, the line y = x+3's y-intercept is (0,3). By changing Y to 0 and solving for X, you can always discover the X-intercept. Likewise, you may always solve for Y while holding X equal to 0 in the equation to determine the Y-intercept.To know more about intercept here
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What is 3 to the 2 exponent?
Answer:
It would be 6 because the exponent is 2 so you multiply 3 twice which equals 6
Step-by-step explanation:
3 to the 2nd exponent is 3^2 = 9.
help me, please i need this by tomorrow and I'm in school
Answer:
1/3
Step-by-step explanation:
please give me brainliest
Answer:
4/16
Step-by-step explanation:
The answer is actually 4/16 because you cannot either divide or multiple by any number to get 4/16.
use pascal’s triangle to expand (z+1)^6
The expansion of (z+1)⁶ = z⁶ + 6z⁵+ 15z⁴ + 20z³+ 15z² + 6z + 1
Pascal's Triangle:A type of number pattern is Pascal's Triangle. The triangle-shaped arrangement of integers known as Pascal's Triangle provides the coefficients for the expansion of any binomial statement.
The arrangement of the numerals creates a triangle when they are reflected. The number 1 is first placed at the top, and then the numbers are arranged in a triangle design.
The expansion of (x + y)ⁿ is is given by
(x + y)ⁿ = a₀xⁿ + a₁xⁿ⁻¹y + a₂xⁿ⁻²y² + … + a[tex]_{n -1}[/tex] xyⁿ⁻¹ + a[tex]_{n}[/tex]yⁿ
Here we have (z+1)⁶
Write out Pascal's triangle starting from 1 and up to 6 rows
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
1 6 15 20 15 6 1
So coefficients of expansion are 1, 6, 15, 20, 15, 6, and 1
(z+1)⁶ = (1)z⁶ + (6)z⁵(1)+ (15)z⁴(1)² + 20z³(1)³ + 15z²(1)⁴ + 6z¹(1)⁵ + (1)z⁰(1)⁶
=> (z+1)⁶ = z⁶ + 6z⁵+ 15z⁴ + 20z³+ 15z² + 6z¹ + 1
Therefore,
The expansion of (z+1)⁶ = z⁶ + 6z⁵+ 15z⁴ + 20z³+ 15z² + 6z + 1
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Can I simplify a function?
The following actions must be taken in order to simplify the rational function f (x) = p (x) q (x): Where q (x) = 0, identify the values of x.
what is functions ?The study of mathematics include the study of numbers, formulas and related structures, forms and the environments in which they exist, quantities and their variations, and the environments in which they exist. A function is an association between a number of inputs, each of which has an output. Simply described, a function is a relationship between inputs and outputs in which each input leads to a single, distinct result. Usually, the letter f is used to denote functions (x). input consists of x. There are four different types of functions. based on the following elements: one-to-one functions, many-to-one functions, on functions, one-to-one functions, and within functions.
given
The following actions must be taken in order to simplify the rational function f (x) = p (x) q (x): Where q (x) = 0, identify the values of x.
If so, all real values, with the exception of these roots, are in the domain of f (x).
It may be necessary to factor by grouping or by applying the factor theorem in order to fully factor both p (x) and q (x).
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How do you write 3 exponents?
To write 3 exponents, you can use the following format: base^exponent.
An exponent is a small number that is written slightly above and to the right of a base number. The base is the number being multiplied, and the exponent tells you how many times the base is being multiplied by itself.
For example, to write 3 raised to the power of 2, you would write it as 3^2, which means 3 multiplied by itself 2 times, which is equal to 9.
It's important to note that the exponent is also known as the power, so 3^2, 3^3 and 3^4 are also read as 3 to the power of 2, 3 to the power of 3, 3 to the power of 4.
In summary, to write 3 exponents, you can use the format: base^exponent, where the base is the number being multiplied and the exponent tells you how many times the base is being multiplied by itself. In this case, 3^2, 3^3, and 3^4 represent 3 multiplied by itself 2, 3, and 4 times respectively.
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Lines AE and GH are parallel in the image below. The image will be used to prove that the sum of the measures or the
interior angles of ACGH is 180°.
Which statement would be included in a proof of why m/C+m/G+mZH= 180
Angles F and C are congruent. An angle inside a form is called an interior angle.
What is interior angle?An angle inside a form is called an interior angle. The closed shape with vertices and sides is called a polygon. Every interior angle of a regular polygon is equal to every other interior angle. For instance, the inner angles of a square are all equal to the right angle, or 90 degrees. A set's interior is comprised of all of its open subsets. The area of a region that is "within" a given border is more often referred to as the interior of a geometric structure. For instance, the interior of a circle and a sphere, respectively, is a (open) disk. Interior angles are the angles created within or inside of a shape. In this case, the interior angles ABC, BCA, and CAB.
From the figure, it can be seen that Angles F and C are opposite angles. Opposite angles are non-adjacent angles formed by two intersecting lines. Opposite angles are congruent .
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Angles F and C are congruent. An angle inside a form is called an interior angle.
What is interior angle?An angle inside a form is called an interior angle. The closed shape with vertices and sides is called a polygon. Every interior angle of a regular polygon is equal to every other interior angle. For instance, the inner angles of a square are all equal to the right angle, or 90 degrees.
A set's interior is comprised of all of its open subsets. The area of a region that is "within" a given border is more often referred to as the interior of a geometric structure. For instance, the interior of a circle and a sphere, respectively, is a (open) disk. Interior angles are the angles created within or inside of a shape. In this case, the interior angles ABC, BCA, and CAB.
From the figure, it can be seen that Angles F and C are opposite angles. Opposite angles are non-adjacent angles formed by two intersecting lines. Opposite angles are congruent .
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What are the formula in coordinate geometry for Class 9?
The formula in coordinate geometry for Class 9 include distance formula, midpoint formula, section formula, equation of a line, slope of a line, equation of a circle, equation of a parabola, equation of an ellipse, equation of a hyperbola, area of a triangle, and area of a circle.
The distance formula is used to determine the distance between two points in a coordinate plane. The midpoint formula is used to find the midpoint between two points. The section formula is used to calculate the area of a triangle formed by three points. The equation of a line is used to define the line in terms of its slope and intercept. The slope of a line is used to calculate the angle of the line in relation to the x-axis. The equation of a circle is used to determine the equation of a circle with a given center and radius. The equation of a parabola is used to determine the equation of a parabola with a given focus and directrix. The equation of an ellipse is used to determine the equation of an ellipse with a given center and major and minor axes. In coordinate geometry the equation of a hyperbola is used to determine the equation of a hyperbola with a given center and asymptotes. The area of a triangle is used to find the area of a triangle given the three vertices. The area of a circle is used to find the area of a circle given the radius.
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A school is paving a new rectangular area to create an additional, flat parking lot for teachers. Which units should the principal use to estimate the number of parking spaces created, and why?
The principal should use Square meters because the average length and width of the parking spaces will determine the number of parking spaces created in the rectangular parking lot.
Parallel parking, perpendicular parking, and angle parking are the three most frequently used parking configurations for the majority of motorized vehicles. These are self-park setups, meaning the driver of the car can go to the parking on their own.The length is typically 16 feet to 18 feet for perpendicular or angled parking spaces. The typical breadth is between 7.9 feet and 9 feet. The standard length and breadth for parallel parking spaces are 20 feet and 7.9 feet, respectively.The required number of stalls times the projected land area per stall will give you the paved area needed for parking. For instance, a 200-spot parking lot will need a paved surface of 65,000 square feet, or approximately, with each stall requiring an estimated 325 square feet of space.To know more about rectangular area here
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A triangle has two sides measuring 8. 5 cm and 15 cm. What are the least and greatest whole number possibilities for the third side? enter your answers in the boxes.
The least whole number possibility for the third side is 8 cm. The greatest whole number possibility for the third side is 22 cm.
A triangle is a three-sided polygon. It is a geometric shape that has three edges and three vertices. Triangles can be classified based on their side lengths (such as equilateral, isosceles, or scalene) or based on the angles between their sides (such as acute, right, or obtuse). Triangles are a fundamental shape in geometry and are used in many branches of mathematics and physics. To form a triangle, the sum of the lengths of any two sides must be greater than the length of the third side.
Using this rule, we can find the possible range of values for the third side of the triangle.
The least possible length of the third side would be:
8.5cm + 15cm - 15cm = 8.5cm
The greatest possible length of the third side would be:
(8.5cm + 15cm) - 1cm = 22.5cm
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What is the equation of this line in slope intercept form?
Answer:
y=-2x+3
Step-by-step explanation:
y=mx+b
Shannon babysits and charges a flat fee of $10 plus $2 for very hour she babysits. She needs to make $72 this week. How many hours can Shannon babysit
Answer:
72 divided by 12 is 6 so 6 hours she needs to babysit
Sergio has p paintings in his art collection. He and other local painting collectors agreed to donate a total of 48 paintings to the local museum. Each of the 12 collectors will donate the same number of paintings How many paintings will Sergio have in his art collection after his donation?
Step-by-step explanation:
The question is a bit confusing, so I am going to reword it to what I assume it means, which is, “Sergio initially has “p” paintings. There are 12 art collectors total, including Sergio. All the art collectors together donate a total of 48 paintings, and each art collector donates the same number of paintings. How many paintings does Sergio have left?”
p = number of Sergio’s paintings at the start.
p-X = the number of Sergio’s paintings at the end.
48 = the total number of paintings donated by all art collectors
12 = number of art collectors
48/12 = 4 = the number of paintings that each art collector donated
4 = X = the number of paintings that Sergio donated
p-4 = the number of paintings Sergio has left (answer)
(My regrets if my understanding of the question was something other than the above.)
1. The population of a town was 5655 in 2010. The population grows at a rate of 1.4% annually. (a) Use the exponential growth model to write an equation that estimates the population t years after 2010. (a) Estimate the population of the town in 2022. Show your work.
(a) The exponential growth model is P = 5655 e^(0.014t)
(b) Population of the town in 2022 is 6689.5065.
What is Population Growth?Population growth is defined as the number of people increasing over years in a specific region calculated using annual growth rate.
(a) The formula to calculate population growth is,
P = P₀ e^(r t)
Given,
Initial population in 2010, P₀ = 5655
Annual growth rate, r = 1.4% = 0.014
Substituting,
P = 5655 e^(0.014t)
(b) To estimate the population of town in 2022,
t = 2022 - 2010 = 12 years
Substituting value of t in the formula in (a),
P = 5655 e^(0.014 × 12)
= 5655 e^(0.168)
= 5655 × 1.1829
= 6689.5065
Hence the population is 6689.5065 in 2022.
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Can someone solve the very first one under the pencil line solve that equation ASAP please
Answer:19.28 or 125/7
Step-by-step explanation:
first, replace all the a's with 1's, the b's with 2's, and the c's with 4's. you end up with (-3(1)+4(2)) ³/2(4)-1
then you would solve that until you get, (-3+8)³/8-1
then, (5)³/7
and once you've solved that you get 19.28 or 125/7
evaluate the expression
A boat travels downstream at an average speed of 30 mph. The boat makes the same trip back upstream at an average speed of 18 mph. What is the speed of the boat? What is the speed of the water current?
Therefore , the solution to the given problem of equation comes out to be is 19 mph for a boat in calm water.
What does equation mean?An equation must always include two equal members and one or more unknown members (the unknown variables). When multiplied by itself, what number, for example, results in 16. To express this maths equation mathematically, use the equation or expression.
Here,
The determining formula is
30/u-4 = 46/u+4
(time equation, where u represents the boat's speed in still water)
Cross-multiply:
30*(u+4) = 46(u-4) (u-4),
30u + 120 = 46u - 184,
120 + 184 = 46u - 30u,
Thus,
304 = 16u
=> 304/16
=> 19.
The answer is 19 mph for a boat in calm water.
Therefore , the solution to the given problem of equation comes out to be is 19 mph for a boat in calm water.
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the average person's heart beats about 4,200 times in 1 hour. Write and solve an equation to find about how many times that is per minute
Lilyan took out a 72-month car loan for $17,595. If he had paid a total of $22,556. 79 at the end of the loan, find the interet rate
Lilyan took out a 72-month car loan for $17,595. If he had paid a total of $22,556. 79 at the end of the loan, then the interet rate is 6.7%
What is principal amount?
The loan amount that the lender gives to the borrower is referred to as the primary amount. Additionally, it is the factor the lender uses to calculate interest.
What is simple interest?
Simple interest is a method to calculate the amount of interest charged on a sum at a given rate and for a given period of time. The formula to calculate simple interest is I=P.r.t
Where P=principal amount, r=rate, t=time.
Lilyan took out a 72-month car loan for $17,595.
If he had paid a total of $22,556. 79 at the end of the loan,
find the interet rate
72 months = 6 years
principal = 17595
amount = 22556.79
we have to calculate interest
A = P ( 1+ r/100) ^ n
= 17595 ( 1+r/100)^6
22556.79/17595 ^ 1/6= 1+0.00r
r= 6.7%
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[Algebra, polynomials] I'd like help with further explanation with what the image is telling me. I understand that you find the GCF of each term, but for the question I don't know why the GCF of the exponents are 3. I thought 4 would be the GCF. I don't think I learned how to find GCF properly.
As for the second image, I just have no clue on how to do it. I don't want just the answer. Anyone good with math please help :)
Answer: For the GCF one, the GCF would be [tex]3y^{3}[/tex] because you are factoring from both [tex]15y^{4}[/tex] and [tex]12y^{3}[/tex], the reason it cannot be [tex]3y^{4}[/tex] is because that exponent value exceeds the exponent value of [tex]12y^{3}[/tex].
Step-by-step explanation:
So when you find a greatest common factor (GCF) you are basically trying to simplify the expression by extracting numbers to put it into its simplest form. The GCF of 15 and 12, is 3. And the GCF of the exponents would be [tex]y^{3}[/tex] .
Two identical springs (x and y) are stretched to different lengths and held there.
The illustration shows that (A) spring x has a higher elastic potential energy.
What is elastic potential energy?The energy that is stored when a force is used to deform an elastic object is known as elastic potential energy.
Until the force is released and the object springs back to its original shape, doing labor in the process, the energy is retained.
Kinetic energy is the power that an object has while in motion.
For instance, a stretched rubber band contains elastic potential energy because, when released, it will spring back to its resting position, converting the potential energy to kinetic energy.
So, according to the given image, spring x has more elastic potential energy.
Therefore, the illustration shows that (A) spring x has a higher elastic potential energy.
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Correct question:
Two identical springs ( x and y ) are stretched to different lengths and held there
Which of the following statements is true
A) spring x has more elastic potential energy
B) spring y has more elastic potential energy
C) spring x has more kinetic energy
D) spring y has more kinetic energy
What are coordinates Class 9?
A series of numbers known as coordinates can be used to display a point's precise location on a coordinate plane. Coordination Plane Definition. The intersection of the x-axis and y-axis, two perpendicular lines that create a 2D plane known as a coordinate plane.
Which coordinate system is used?There are three types of co-ordinates are:
(i) Cartesian co-ordinates
(ii) cylindrical co-ordinates
(iii) spherical co-ordinates
The Cartesian coordinate system is a prime example of a coordinate system. Two perpendicular lines are picked in the plane, and a point's coordinates are assumed to be the signed distances between the lines.
Coordinates are a pair of integers (also known as Cartesian coordinates), or occasionally a letter and a number, that identify a specific point on a grid, also known as a coordinate plane. Two axes, the x (horizontal) and y (vertical), and four quadrants make up a coordinate plane (vertical).
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What is the solution to the equation 1 h 5 2 h 5 16 h 2 25?
The solution to the equation 1/h-5+2/h+5=16/h^2-25 is H=7 .
What is the answer to the equation?An equation’s solution is an array of all values that, when substituted for unknowns, make the equation true. To solve equations with one unknown raised to a power of one, two basic algebra methods using the additive and multiplicative properties are needed. The set of linear equations has three alternative solutions.
They are as follows:
One-of-a-kind solution.
There is no solution.
There are an infinite number of solutions.
False solutions are ones that do not fundamentally address the problem at hand but fool others into believing they do, while also causing additional major problems.
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Angela wants to know how many of the 380 7th graders earned an A on the last Science test. She decides to sample 15% of the 7th graders in order to predict how many earned an A. What is her sample size?
Angela's sample size for the study on predicting how many 7th graders earned an A, is 57 students
How to find the sample size ?The number of observations used to calculate estimates for a certain population is known as the sample size. The sample size was determined by drawing from the population. Sampling is the practice of choosing a portion of the population from which to draw conclusions about the characteristics of the entire population.
In engaging in sampling, Angela wanted to sample 15 % of the 7th graders which means that her sample size would be :
= Percentage to be sampled x Number of 7th graders
= 15 % x 380
= 57 students
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A repair person charges a travel fee to visit a home and an hourly fee for the time spent fixing a leak.
A repair that takes 2 h costs $100. A repair that takes 6 h costs $260.
Write an equation to represent the total cost of a repair, y, as a function of the
number of hours spent fixing a leak.
So on solving the provided question, we can say that y = a + xb is the necessary equation for the total fee the repairman charged, y = 260 + 6x
What is equation?A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.
Here,
Let the total amount charged by the repairman be y and the total number of hours worked be x,
[tex]y = a + xb[/tex]
a is as travel fee
b is as hourly rate
Therefore, y = a + xb is the necessary equation for the total fee the repairman charged.
y = 260 + 6x
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What to do if the bases and exponents are different?
If the bases of two exponential expressions are different, they cannot be directly compared or combined.
THE BASE AND EXPONENTSYou can convert one of the bases to match the other by using logarithm properties. For example, if you want to compare or combine 2³ and 3², you can convert the base of one of them to match the other by using the logarithm property log3(3²) = 2, so 3² can be rewritten as 2^(log3(3²)) = 2².
If you want to add or subtract exponential expressions with different bases, you can convert one of the bases to match the other by using logarithm properties, then combine the exponents. For example, if you want to add 2³ and 3², you can convert the base of one of them to match the other by using the logarithm property log2(3) = 1.58496, so 3² can be rewritten as 2^(log2(3)*2) = 2^3.18992. Now you can add the two exponents: 2³ + 2^3.18992 = 2³ (1 + 2^0.18992).
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Solve the equation, and check your solution.
8.4+
8.4 = 1.4x
8.4+
—
= 1.4x +
= X
Complete the solution using inverse relationships.
8.4 = 1.4x
= 1.4x +
= X
-
(Type whole numbers or decimals.)
The solution to the equation 8.4 = 1.4x for the unknown variable x is 6.
How to solve equation?8.4 = 1.4x
divide both sides by the variable of x
x = 8.4 / 1.4
x = 6
Check:
8.4 = 1.4x
8.4 = 1.4(6)
8.4 = 8.4
Using inverse relationship
8.4 = k / 1.4
cross product
8.4 × 1.4 = k
11.76 = k
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How do you write a polynomial function with factors?
So on provided question we cans ay that Take the common binomial into account. Note that when we multiply our response by itself, the original polynomial results.
what are polynomials?A mathematical expression made up of coefficients and uncertainty that only makes use of additions, subtractions, multiplications, and positive integer powers of variables is known as a polynomial. The formula x2 4x + 7 denotes a single indeterminate x polynomial. An expression in mathematics known as a polynomial is made up of variables (also known as indeterminates) and coefficients that may be added, subtracted, multiplied, and raised to negative integer powers of non-variables. An algebraic statement with variables and coefficients is called a polynomial. An expression can only contain the operations addition, subtraction, multiplication, and non-negative integer exponents. Polynomials are the name for these expressions.
here,
Group the first two terms first, followed by the last two terms. Remove a GCF from each each binomial. Take the common binomial into account. Note that when we multiply our response by itself, the original polynomial results.
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-91x-13x= 276.50
Show work
Answer:
x = -2.65865384615
Step-by-step explanation:
-91x - 13x = 276.50
First, Combine Like Terms
-91x + (-13x) = -104x
-104x = 276.50
Second, divide
276.50 / -104 = x
x = -2.65865384615
In ΔTUV, u = 750 cm, mm∠T=105° and mm∠U=42°. Find the length of t, to the nearest centimeter.
The length of t to the nearest centimeter is 1083 cm.
What are Angles?Angles are the figure formed by the intersection of two lines or rays by sharing a common point. This point is called the vertex of the angle.
Given that,
u = 750 cm
m ∠U = 42°
m ∠T = 105°
We have the sine rule to find missing length as,
[tex]\frac{u}{sin U}[/tex] = [tex]\frac{t}{sin T}[/tex]
Substituting the measures given,
[750 / sin (42°)] = [t / sin (105°)]
Cross multiplying,
t = [ 750 × sin (105°)] / sin (42°)
t = 1082.59 ≈ 1083 cm
Hence the length of the missing side is 1083 cm.
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