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Right Triangle Relationships and Trigonometry — Test Answers

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

A
The hypotenuse is line segment QR .
B
The side opposite angle cap q is line segment RS .
C
The side opposite angle cap r is line segment RQ .
D
The side adjacent to angle cap q is line segment QS .
E
The side adjacent to angle cap r is line segment SQ .
3

Which equation correctly uses the law of cosines to solve for y ?

A
9 squared is equal to y squared plus 19 squared minus 2 y 19 cosine open paren 41 degrees close paren
B
y squared is equal to 9 squared plus 19 squared minus 2 9 19 cosine open paren 41 degrees close paren
C
9 squared is equal to y squared plus 19 squared minus 2 9 19 cosine open paren 41 degrees close paren
D
y squared is equal to 9 squared plus 19 squared minus 2 y 19 cosine open paren 41 degrees close paren
4

What is the area of triangle PQR ? Round to the nearest tenth of a square unit.

A
185 point 4 square units
B
111 point 3 square units
C
222 point 5 square units
D
70 point 5 square units
6

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

A
sine of x is equal to 15 tenths
B
cosine of x is equal to 15 tenths
C
sine of x is equal to 10 over 15
D
cosine of x is equal to 10 over 15
7

What is the measure of angle cap n to the nearest whole degree?

A
65 degrees
B
55 degrees
C
35 degrees
D
45 degrees
8

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

A
21 point 3 in.
B
23 point 5 in.
C
19 point 3 in.
D
68 point 0 in.
12

What is the length of one leg of the triangle?

A
11 square root of 2 units
B
22 units
C
11 units
D
22 square root of 2 units
13

What are the angle measures of triangle VUW ?

A
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
B
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
C
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
D
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
14

What is the length of line segment AB ?

A
4 inches
B
4 square root of 3 inches
C
1 inch
D
square root of 3 inches
17

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 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.
B
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.
C
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.
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 opposite to the side with length 3 point 1 is labeled as x.
18

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

A
10 times cosine times open paren 40 degrees close paren is equal to AC
B
the fraction with numerator 10 and denominator mathrm cosine open paren 40 raised to the mathrm o power close paren is equal to AC
C
the fraction with numerator 10 and denominator mathrm sine 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
19

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
acute, because 12 squared plus 15 squared is greater than 10 squared
C
obtuse, because 10 squared plus 12 squared is greater than 15 squared
D
acute, because 10 squared plus 12 squared is greater than 15 squared
20

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 A over 12
B
tangent of open paren 22.6 degrees close paren is equal to A over 13
C
tangent of open paren 22.6 degrees close paren is equal to 12 over A
D
tangent of open paren 22.6 degrees close paren is equal to 13 over A

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