AnswersFall 24 GMS Geometry Concepts and Connections BSolving for Angle Measures of Right Triangles

Solving for Angle Measures of Right Triangles — Unit test Answers

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Triangle L J K is shown. Angle J L K is a right angle. The length of the hypotenuse is 15 inches and the length of the side adjacent to the right angle is 10 inches. The angle between the 2 sides is x.

Question illustration
A
sin(x) =
Option A
B
sin(x) =
Option B
C
cos(x) =
Option C
D
cos(x) =
Option D
2
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In right triangle XYZ, the right angle is located at vertex Y. The length of line segment XY is 12.4 cm. The length of line segment YZ is 15.1 cm.

A
34.8°
B
39.4°
C
50.6°
D
55.2°
3

Joey is building a frame for a sandbox. The sandbox is going to be a quadrilateral that has the lengths shown.

Question illustration
A
a rectangle, because angle C is a right angle
B
a rectangle, because angle C and angle X are congruent
C
a quadrilateral, because angle C and angle X are acute
D
a quadrilateral, because angle C and angle X are obtuse
4

A right triangle has one angle that measure 23o. The adjacent leg measures 27.6 cm and the hypotenuse measures 30 cm.What is the approximate area of the triangle? Round to the nearest tenth.Area of a triangle = bh

Question illustration
A
68.7 cm2
B
161.8 cm2
C
381.3 cm2
D
450.0 cm2
5

Triangle ABC is a right triangle and cos(22.6o)=. Solve for b and round to the nearest whole number.

Question illustration
A
tan(22.6o) =
Option A
B
tan(22.6o) =
Option B
C
tan(22.6o) =
Option C
D
tan(22.6o) =
Option D
6

In right triangle XYZ, the right angle is located at vertex Y. The length of line segment XY is 12.4 cm. The length of line segment YZ is 15.1 cm.

A
34.8°
B
39.4°
C
50.6°
D
55.2°
7

Which statements are true about triangle QRS? Select three options.

A
The side opposite ∠Q is RS.
B
The side opposite ∠R is RQ.
C
The hypotenuse is QR.
D
The side adjacent to ∠R is SQ.
E
The side adjacent to ∠Q is QS.
8

Triangle A B C is shown. Angle B C A is a right angle. The length of hypotenuse A B is 26, the length of A C is 10, and the length of B C is 24.

Question illustration
A
Five-thirteenths
Option A
B
Twelve-thirteenths
Option B
C
Twelve-fifths
Option C
D
Thirteen-twelfths
Option D
9

A right triangle is shown. The length of the hypotenuse is 4 centimeters and the lengths of the other 2 sides are congruent.

Question illustration
A
2 cm
B
cm
Option B
C
4 cm
D
cm
Option D
10

The hypotenuse of a 45°-45°-90° triangle measures units.

Question illustration
A
11 units
B
units
Option B
C
22 units
D
units
Option D
11

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
2.4 inches
B
3.2 inches
C
10.0 inches
D
15.7 inches
12

The equation can be used to find the length of .

Question illustration
A
19.3 in.
B
21.3 in.
C
23.5 in.
D
68.0 in.
13

Which statements are true about triangle QRS? Select three options.

A
The side opposite ∠Q is RS.
B
The side opposite ∠R is RQ.
C
The hypotenuse is QR.
D
The side adjacent to ∠R is SQ.
E
The side adjacent to ∠Q is QS.
14

Which equation can be used to find the length of ?

Question illustration
A
(10)sin(40o) = AC
B
(10)cos(40o) = AC
C
= AC
Option C
D
= AC
Option D
15

Triangle V U W is shown. The length of side W V is 6 centimeters, the length of side W U is 3 StartRoot 3 EndRoot centimeters, and the length of side U V is 3 centimeters.

Question illustration
A
m∠V = 30°, m∠U = 60°, m∠W = 90°
B
m∠V = 90°, m∠U = 60°, m∠W = 30°
C
m∠V = 30°, m∠U = 90°, m∠W = 60°
D
m∠V = 60°, m∠U = 90°, m∠W = 30°
16

Which classification best represents a triangle with side lengths 10 in., 12 in., and 15 in.?

A
acute, because 102+122>152
B
acute, because 122+152>102
C
obtuse, because 102+122>152
D
obtuse, because 122+152>102
17

Triangle D E F is shown. Angle F D E is a right angle. The length of D E is 40, the length of D F is 9, and the length of hypotenuse F E is 41.

Question illustration
A
StartFraction 9 Over 41 EndFraction
Option A
B
StartFraction 40 Over 41 EndFraction
Option B
C
StartFraction 40 Over 9 EndFraction
Option C
D
StartFraction 41 Over 9 EndFraction
Option D
18

The diagonal of rectangle ABCD measures 2 inches in length.

Question illustration
A
1 inch
B
inches
Option B
C
4 inches
D
inches
Option D
19

Use the diagram to complete the statement.

Question illustration
A
cos(38°).
B
cos(52°).
C
tan(38°).
D
tan(52°).
20

In which triangle is the value of x equal to tan−1? (Images may not be drawn to scale.)

Question illustration
A
A right triangle is shown. The length of the hypotenuse is 5.2 and the length of the side adjacent to the right angle is 3.1. The angle between the 2 sides is x.
Option A
B
A right triangle is shown. The length of the hypotenuse is 5.2 and the length of the side adjacent to the right angle is 3.1. The angle opposite to side with length 3.1 is x.
Option B
C
A right triangle is shown. The length of 2 sides are 5.2 and 3.1. The angle opposite to side with length 5.2 is x.
Option C
D
A right triangle is shown. The length of 2 sides are 5.2 and 3.1. The angle opposite to side with length 3.1 is x.
Option D

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