AnswersGeometryRight Triangle Relationships and Trigonometry

Right Triangle Relationships and Trigonometry — Test Answers

24 verified answers
1
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Which statements are true about triangle QRS ? Choose three correct answers.

A
The side adjacent to angle cap r is line segment SQ .
B
The side adjacent to angle cap q is line segment QS .
C
The hypotenuse is line segment QR .
D
The side opposite angle cap q is line segment RS .
E
The side opposite angle cap r is line segment RQ .
2
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If the diagonal of the sandbox measures 14 feet, which best describes the shape of the sandbox?

A
a quadrilateral, because angle cap c and angle cap x are obtuse
B
a rectangle, because angle cap c is a right angle
C
a quadrilateral, because angle cap c and angle cap x are acute
D
a rectangle, because angle cap c and angle cap x are congruent
3

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

A
5 over 13
B
12 fifths
C
12 over 13
D
13 over 12
4

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

A
40 over 41
B
41 ninths
C
9 over 41
D
40 ninths
5

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

A
tangent 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
cosine of open paren 38 degrees close paren .
6

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 30 degrees , m angle cap u is equal to 60 degrees , m angle cap w is equal to 90 degrees
C
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
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
7

What is the measure of angle LKJ ? Round to the nearest whole degree.

A
55 degrees
B
49 degrees
C
41 degrees
D
45 degrees
8

What are the values of m and theta in the given diagram?

A
m is equal to the fraction with numerator square root of 3 and denominator 3 , theta is equal to pi over 6
B
m is equal to the fraction with numerator square root of 3 and denominator 2 , theta is equal to pi over 3
C
m is equal to the fraction with numerator square root of 3 and denominator 2 , theta is equal to pi over 6
D
m is equal to the fraction with numerator square root of 3 and denominator 3 , theta is equal to pi over 3
9

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
cosine of x is equal to 10 over 15
D
sine of x is equal to 10 over 15
10

What is the length of one leg of the triangle?

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

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

The hypotenuse of a 45 degrees - 45 degrees - 90 degrees triangle measures 4 cm. What is the length of one leg of the triangle?

A
2 square root of 2 cm
B
4 cm
C
2 cm
D
4 square root of 2 cm
13

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

A
23 point 5 in.
B
21 point 3 in.
C
68 point 0 in.
D
19 point 3 in.
14

Which of the following best explains the value of sine pi over 3 on the given unit circle?

A
sine pi over 3 is equal to opposite over hypotenuse is equal to opposite over 1 is equal to opposite The length opposite the angle is the vertical distance from the x -axis on the graph.
B
sine pi over 3 is equal to adjacent over hypotenuse is equal to adjacent over 1 is equal to adjacent The length adjacent to the angle is the vertical distance from the x -axis on the graph.
C
sine pi over 3 is equal to adjacent over hypotenuse is equal to adjacent over 1 is equal to adjacent The length adjacent to the angle is the horizontal distance from the y -axis on the graph.
D
sine pi over 3 is equal to opposite over hypotenuse is equal to opposite over 1 is equal to opposite The length opposite the angle is the horizontal distance from the y -axis on the graph.
15

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
2 point 4 inches
B
15 point 7 inches
C
10 point 0 inches
D
3 point 2 inches
16

The angle measures associated with which set of ordered pairs share the same reference angle?

A
open paren 1 half comma negative the fraction with numerator square root of 3 and denominator 2 close paren , open paren negative the fraction with numerator square root of 3 and denominator 2 comma 1 half close paren
B
open paren negative 1 half comma negative the fraction with numerator square root of 3 and denominator 2 close paren , open paren 1 half comma the fraction with numerator square root of 3 and denominator 2 close paren
C
open paren the fraction with numerator square root of 3 and denominator 2 comma 1 half close paren , open paren 1 half comma the fraction with numerator square root of 3 and denominator 2 close paren
D
open paren negative the fraction with numerator square root of 3 and denominator 2 comma negative 1 half close paren , open paren negative 1 half comma negative the fraction with numerator square root of 3 and denominator 2 close paren
17

If cosine theta almost equal to 0 point 3 0 9 0 , which of the following represents approximate values of sine theta and tangent theta , for 0 degrees is less than theta comma theta is less than 90 degrees ?

A
sine theta almost equal to 0 point 9 5 1 1 ; tangent theta almost equal to 0 point 3 2 4 9
B
sine theta almost equal to 3 point 2 3 6 2 ; tangent theta almost equal to 0 point 0 9 5 5
C
sine theta almost equal to 0 point 9 5 1 1 ; tangent theta almost equal to 3 point 0 7 8 0
D
sine theta almost equal to 3 point 2 3 6 2 ; tangent theta almost equal to 10 point 4 7 3 1
18

Three trigonometric functions for a given angle are shown. cosecant theta is equal to 13 over 12 , secant theta is equal to negative 13 fifths , cotangent theta is equal to negative 5 over 12 What are the coordinates of point open paren x comma y close paren on the terminal ray of angle theta , assuming that the values above were not simplified?

A
open paren negative 5 comma 12 close paren
B
open paren 12 comma negative 5 close paren
C
open paren negative 12 comma 5 close paren
D
open paren 5 comma negative 12 close paren
19

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 sine times open paren 40 degrees close paren is equal to AC
C
10 times cosine times open paren 40 degrees close paren is equal to AC
D
the fraction with numerator 10 and denominator mathrm cosine open paren 40 raised to the mathrm o power close paren is equal to AC
20

Consider the relationship, given pi over 2 is less than theta comma theta is less than pi sine squared theta plus cosine squared theta is equal to 1 Which of the following best explains how this relationship and the value of sine theta can be used to find the other trigonometric values?

A
The values of sine theta and cosine theta represent the legs of a right triangle with a hypotenuse of negative 1 , since theta is in Quadrant II; therefore, solving for cosine theta finds the unknown leg, and then all other trigonometric values can be found.
B
The values of sine theta and cosine theta represent the angles of a right triangle; therefore, other pairs of trigonometric ratios will have the same sum, 1 , which can then be used to find all other values.
C
The values of sine theta and cosine theta represent the angles of a right triangle; therefore, solving the relationship will find all three angles of the triangle, and then all trigonometric values can be found.
D
The values of sine theta and cosine theta represent the legs of a right triangle with a hypotenuse of 1 ; therefore, solving for cosine theta finds the unknown leg, and then all other trigonometric values can be found.

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