AnswersCARE_24_25_TX-Mathematical Models with Applications AUnit Test

Unit Test Answers

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A ship’s sonar detects a submarine 880 feet below a point on the ocean’s surface 1450 ft dead ahead of the ship. To the nearest degree, find the angle x.

Question illustration
A
59º
B
37º
C
31º
D
53º
2
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Use the diagram to complete the statement.

Question illustration
A
cos(38°).
B
cos(52°).
C
tan(38°).
D
tan(52°).
3

Which of the following statements is true?

A
sin 30° = cos 30°
B
sin 35° = cos 55°
C
sin 60° = cos 60°
D
sin 55° = cos 25°
4

Find sin–10.9563 to the nearest degree.

A
17°
B
73°
C
28°
D
13°
5

A kite is currently flying at an altitude of 19 meters above the ground. If the angle of elevation from the ground to the kite is , find the length of the kite string to the nearest meter.

Question illustration
A
35 meters
B
23 meters
C
10 meters
D
29 meters
6

a. c. b. d. Please select the best answer from the choices provided

Question illustration
A
A
B
B
C
C
D
D
7

Use a calculator to find the approximate value of the expression. Round the answer to two decimal places. The sine of the complementary angle to 75°

A
0.65
B
0.57
C
0.34
D
0.26
8

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.
9

Evaluate the function requested. Write your answer as a fraction in lowest terms. Find sin A. a. c. b. d. Please select the best answer from the choices provided

Question illustration
A
A
B
B
C
C
D
D
10

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
11

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
12

Use the diagram of the right triangle above and round your answer to the nearest hundredth. If º and a = 10 meters, find b.

Question illustration
A
17.32 m
B
6.93 m
C
14 m
D
9.99 m
13

You are sailing from your lakeshore cabin to a marina 60º north of east and 0.5 miles across the lake. On your return trip, you decide to sail directly south and then west to get back to your cabin. Which of the following expressions uses the complementary angle of 60° to determine how far you would travel on your trip west?

Question illustration
A
0.5cos30°
B
0.5cos60°
C
0.5sin30°
D
0.5sin60°
14

Two students describe the sides of right triangle ABC in relation to ∠B. TomasAB is the hypotenuse.AC is the opposite side.BC is the adjacent side.IlianaAB is the hypotenuse.BC is the opposite side.AC is the adjacent side.Who is correct? Explain.

Question illustration
A
Tomas is correct; AC is opposite ∠B and BC is adjacent to ∠B.
B
Iliana is correct; BC is opposite ∠B and AC is adjacent to ∠B.
C
Both are correct because both AC and BC are opposite ∠B.
D
Neither is correct because neither AC nor BC is opposite ∠B.
15

Given , determine and exactly.

Question illustration
A
and
B
and
C
and
D
and
16

Solve for x. Round your answer to the nearest thousandth.

Question illustration
A
7.08
B
23.869
C
8.442
D
10.903
17

Which of the following statements is true?

A
sin 18° = cos 72°
B
sin 55° = cos 55°
C
sin 72° = cos 18°
D
Both a and c.
18

If the cotangent and tangent are reciprocals of each other, then what is the cotangent of an angle if the tangent of the same angle is where a and b are not zero? a. c. b. d. Please select the best answer from the choices provided

Question illustration
A
A
B
B
C
C
D
D
19

Which is NOT an example of the three trigonometric reciprocals of sine, cosine and tangent?

A
cosecant
B
secant
C
theorem
D
cotangent
20

Which of the following expressions is equal to the height, h, of this triangle?

Question illustration
A
25(cos34°)
B
25(cos56°)
C
25(tan34°)
D
25(tan56°)

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