AnswersGeometry with StatisticsRight Triangle Relationships and Trigonometry

Right Triangle Relationships and Trigonometry — Test Answers

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Which equation correctly uses the value of b to solve for A ?

A
tangent of open paren 22.6 degrees close paren is equal to 13 over A
B
tangent of open paren 22.6 degrees close paren is equal to 12 over A
C
tangent of open paren 22.6 degrees close paren is equal to A over 13
D
tangent of open paren 22.6 degrees close paren is equal to A over 12
2
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Which classification best represents a triangle with side lengths 10 in., 12 in., and 15 in.?

A
obtuse, because 12 squared plus 15 squared is greater than 10 squared
B
obtuse, because 10 squared plus 12 squared is greater than 15 squared
C
acute, because 12 squared plus 15 squared is greater than 10 squared
D
acute, because 10 squared plus 12 squared is greater than 15 squared
3

A builder needs three pipes of different lengths. The pipes are 6 square root of 96 feet long, 12 square root of 150 feet long, and 2 square root of 294 feet long. How many feet of piping is required in all? (Hint: Try dividing each radicand by 6 )

A
20 square root of 540 feet
B
20 square root of 294 feet
C
98 square root of 6 feet
D
20 square root of 6 feet
4

Simplify square root of 18

A
3 square root of 2
B
2 square root of 9
C
9 square root of 2
D
2 square root of 3
5

Combine and simplify these radicals . square root of 8 times end root square root of 20

A
10 square root of 4
B
160
C
40
D
4 square root of 10
6

An acute triangle has side lengths 21 cm, x cm, and 2 x cm. If 21 is one of the shorter sides of the triangle, what is the greatest possible length of the longest side, rounded to the nearest tenth?

A
24 point 2 cm
B
18 point 8 cm
C
42 point 0 cm
D
72 point 7 cm
7

In right triangle XYZ , the right angle is located at vertex cap y The length of line segment XY is 12 point 4 cm. The length of line segment YZ is 15 point 1 cm. Which is the approximate measure of angle YZX ?

A
39.4 degrees
B
55.2 degrees
C
50.6 degrees
D
34.8 degrees
8

Which equation can be used to find the length of line segment AC ? Expand Image

A
the fraction with numerator 10 and denominator mathrm sine open paren 40 raised to the mathrm o power close paren is equal to AC
B
10 times cosine times open paren 40 degrees close paren is equal to AC
C
the fraction with numerator 10 and denominator mathrm cosine open paren 40 raised to the mathrm o power close paren is equal to AC
D
10 times sine times open paren 40 degrees close paren is equal to AC
9

The lengths of two sides of a right triangle are 5 inches and 8 inches. What is the difference between the two possible lengths of the third side of the triangle? Round your answer to the nearest tenth.

A
10 point 0 inches
B
3 point 2 inches
C
15 point 7 inches
D
2 point 4 inches
10

In which triangle is the value of x equal to tangent inverse of open paren 3 point 1 over 5 point 2 close paren ? (Images may not be drawn to scale.)

A
Image with description A right triangle is shown. The length of 2 sides are 5 point 2 and 3 point 1. The angle opposite to side with length 3 point 1 is labeled as x.
B
Image with description A right triangle is shown. The length of the hypotenuse is 5 point 2 and the length of the side adjacent to the right angle is 3 point 1. The angle opposite to the side with length 3 point 1 is labeled as x.
C
Image with description A right triangle is shown. The length of the 2 sides are 5 point 2 and 3 point 1. The angle opposite to the side with length 5 point 2 is labeled as x.
D
Image with description A right triangle is shown. The length of the hypotenuse is 5 point 2 and the length of the side adjacent to the right angle is 3 point 1. The angle between the 2 sides is labeled as x.
11

Simplify square root of 16 y to the 16th power end root

A
8 y to the 8th power
B
4 y to the 8th power
C
8 y to the 4th power
D
4 y to the 4th power
12

A right triangle has one angle that measure 23 degrees The adjacent leg measures 27 point 6 cm and the hypotenuse measures 30 cm. What is the approximate area of the triangle? Round to the nearest tenth. Area of a triangle is equal to 1 half b h

A
161 point 8 cm squared
B
450 point 0 cm squared
C
381 point 3 cm squared
D
68 point 7 cm squared
13

What is the length of the hypotenuse?

A
12 square root of 2 cm
B
6 square root of 2 cm
C
12 cm
D
6 cm
14

Given right triangle ABC , what is the value of tangent of cap A ?

A
13 over 12
B
12 over 13
C
5 over 13
D
12 fifths
15

Given right triangle DEF , what is the value of tangent of cap f ?

A
41 ninths
B
40 ninths
C
9 over 41
D
40 over 41
16

Which statements are true about triangle QRS ? Choose three correct answers.

A
The side adjacent to angle cap q is line segment QS .
B
The hypotenuse is line segment QR .
C
The side opposite angle cap r is line segment RQ .
D
The side opposite angle cap q is line segment RS .
E
The side adjacent to angle cap r is line segment SQ .
17

What is the length of line segment AB ? Round to the nearest tenth.

A
21 point 3 in.
B
23 point 5 in.
C
68 point 0 in.
D
19 point 3 in.
18

What are the angle measures of triangle VUW ?

A
m angle cap v is equal to 60 degrees , m angle cap u is equal to 90 degrees , m angle cap w is equal to 30 degrees
B
m angle cap v is equal to 90 degrees , m angle cap u is equal to 60 degrees , m angle cap w is equal to 30 degrees
C
m angle cap v is equal to 30 degrees , m angle cap u is equal to 60 degrees , m angle cap w is equal to 90 degrees
D
m angle cap v is equal to 30 degrees , m angle cap u is equal to 90 degrees , m angle cap w is equal to 60 degrees
19

Which equation can be used to find the measure of angle LJK ?

A
cosine of x is equal to 10 over 15
B
sine of x is equal to 15 tenths
C
cosine of x is equal to 15 tenths
D
sine of x is equal to 10 over 15
20

Given triangle JKL , sine of open paren 38 degrees close paren equals

A
cosine of open paren 38 degrees close paren .
B
tangent of open paren 52 degrees close paren .
C
cosine of open paren 52 degrees close paren .
D
tangent of open paren 38 degrees close paren .

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