AnswersGeometry ACPA 2026Unit Test

Classifying Quadrilaterals 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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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
3

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.
4

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
5

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
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

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
8

The equation can be used to find the measure of angle LKJ.

Question illustration
A
41°
B
45°
C
49°
D
55°
9

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.
10

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
11

Use the diagram to complete the statement.

Question illustration
A
cos(38°).
B
cos(52°).
C
tan(38°).
D
tan(52°).
12

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
13

Which trigonometric ratios are correct for triangle ABC? Select three options.

A
sin(C) =
Option A
B
cos(B) =
Option B
C
tan(C) =
Option C
D
sin(B) =
Option D
E
tan(B) =
Option E
14

Right triangle ABC is shown.

Question illustration
A
sin(50o) =
Option A
B
sin(50o) =
Option B
C
cos(50o) =
Option C
D
cos(50o) =
Option D
15

Which relationship in the triangle must be true?

Question illustration
A
sin(B) = sin(A)
B
sin(B) = cos(90 – B)
C
cos(B) = sin(180 – B)
D
cos(B) = cos(A)
16

The length of the hypotenuse, line segment AC, in right triangle ABC is 25 cm. The length of line segment BC is 15 cm.

A
31.0°
B
36.9°
C
53.1°
D
59.0°
17

Which equation can be solved to find one of the missing side lengths in the triangle?

Question illustration
A
cos(60o) =
Option A
B
cos(60o) =
Option B
C
cos(60o) =
Option C
D
cos(60o) =
Option D
18

Which expressions can be used to find m∠BAC? Select three options.

A
cos−1
Option A
B
cos−1
Option B
C
sin−1
Option C
D
sin−1
Option D
E
tan−1
Option E
19

The equation can be used to determine the length of line segment AC.

Question illustration
A
11.8 cm
B
12.9 cm
C
14.9 cm
D
15.3 cm
20

A right triangle has one side that measures 4 in. The angle opposite that side measures 80o.What is the length of the hypotenuse of the triangle? Round to the nearest tenth.

A
3.9 in.
B
4.1 in.
C
22.7 in.
D
23.0 in.

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