Name: ________________________ Class: ___________________ Date: __________ ID: A

1

Practice Test

____ 1. What is the reference angle for 15° in standard position?

A 255° B 30° C 345° D 15°

____ 2. What is the reference angle for 200° in standard position?

A 100° B 70° C 20° D 110°

____ 3. What are the three other angles in standard position that have a reference angle of 54°?

A 99°, 144°, 234° B 108°, 162°, 216° C 144°, 234°, 324° D 126°, 234°, 306°

____ 4. What is the exact sine of ∠A?

A 1/ 3 B 1/3 C 2/ 3 D 1/2

____ 5. Solve to the nearest tenth of a unit for the unknown side in the ratio

a

sin30°=

12

sin115°.

A 24 B 21.8 C 6.6 D 24.6

Name: ________________________ ID: A

2

____ 6. The coordinates of a point P on the terminal arm of an angle are shown. What are the exact trigonometric

ratios for sinθ, cos θ, and tanθ?

A sin A = −4

5, cos A =

3

5, tan A = −

4

3 B sin A =

5

3, cos A = −

5

4, tan A = −

3

4

C sin A =3

5, cos A = −

4

5, tan A = −

3

4 D sin A =

4

5, cos A = −

3

5, tan A = −

3

4

____ 7. Which strategy would be best to solve for x in the triangle shown?

A cosine law B primary trigonometric ratios C sine law D none of the above

Name: ________________________ ID: A

3

____ 8. Which strategy would be best to use to solve for x?

A primary trigonometric ratios B sine law C cosine law D none of the above

____ 9. While flying, a helicopter pilot spots a water tower that is 7.4 km to the north. At the same time, he sees a

monument that is 8.5 km to the south. The tower and the monument are separated by a distance of 11.4

km along the flat ground. What is the angle made by the water tower, helicopter, and monument?

A 91° B 11° C 40° D 48°

____ 10. What is the exact cosine of ∠A?

A 2 B 1 C 18 D 1

2

Name: ________________________ ID: A

4

11. Given that sinA =5

12 and that ∠A is located in the second quadrant, determine exact values for the other

two primary trigonometric ratios.

12. A survey of a plot of land is shown. The plot is to have a hedge along its border. How many linear metres

of hedge are needed, to the nearest tenth of a metre?

Name: ________________________ ID: A

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13. A drive belt wraps around three pulleys, A, B, and C, as shown.

What is the measure of ∠A?

Name: ________________________ ID: A

6

14. The point (–5, 7) is located on the terminal arm of ∠A in standard position.

a) Determine the primary trigonometric ratios for ∠A.

b) Determine the primary trigonometric ratios for an ∠B that has the same sine as ∠A, but different signs

for the other two primary trigonometric ratios.

c) Use a calculator to determine the measures of ∠A and ∠B, to the nearest degree.

15. Gursant and Leo are both standing on the north side of a monument that is 6.0 m tall. Leo is standing 3.5

m closer to the monument than Gursant. Leo measures the angle from the ground to the top of the

monument to be 41°. Determine the angle that Gursant would measure from the ground to the top of the

monument, to the nearest degree.

Name: ________________________ ID: A

7

16. In ABC, c = 11 cm, b = 7 cm, and ∠B = 38°.

a) Sketch possible diagrams for this situation.

b) Determine the measure of ∠C in each diagram.

c) Find the measure of ∠A in each diagram.

Name: ________________________ ID: A

8

d) Calculate the length of BC in each diagram.

ID: A

1

Practice Test

Answer Section

1. ANS: D PTS: 1 DIF: Easy OBJ: Section 2.1

NAT: T 1 TOP: Angles in Standard Position KEY: reference angle | < 180°

2. ANS: C PTS: 1 DIF: Easy OBJ: Section 2.1

NAT: T 1 TOP: Angles in Standard Position KEY: reference angle | > 180°

3. ANS: D PTS: 1 DIF: Average OBJ: Section 2.1

NAT: T 1 TOP: Angles in Standard Position KEY: reference angle

4. ANS: D PTS: 1 DIF: Average OBJ: Section 2.1

NAT: T 1 TOP: Angles in Standard Position KEY: special angles | sine

5. ANS: C PTS: 1 DIF: Easy OBJ: Section 2.3

NAT: T 3 TOP: The Sine Law KEY: sine law | side length

6. ANS: C PTS: 1 DIF: Average OBJ: Section 2.2

NAT: T 1 TOP: Trigonometric Ratios of Any Angle

KEY: point on terminal arm | cosine | sine | tangent

7. ANS: C PTS: 1 DIF: Easy OBJ: Section 2.3

NAT: T 3 TOP: The Sine Law KEY: sine law | solution method

8. ANS: C PTS: 1 DIF: Easy OBJ: Section 2.4

NAT: T 3 TOP: The Cosine Law KEY: cosine law | solution method

9. ANS: A PTS: 1 DIF: Average OBJ: Section 2.4

NAT: T 3 TOP: The Cosine Law KEY: cosine law | angle measure

10. ANS: D PTS: 1 DIF: Easy OBJ: Section 2.1

NAT: T 1 TOP: Angles in Standard Position KEY: special angles | cosine

ID: A

2

11. ANS:

Since sinA =y

r, then y = 5 and r = 12.

So,

x2

+ y2

= r2

x2

+ 52

= 122

x2

= 144 − 25

= 119

x = ± 119

Since the angle is in the second quadrant, x = − 119 .

Therefore, cos A = −119

12 and tanA = −

5

119.

PTS: 1 DIF: Average OBJ: Section 2.2 NAT: T 2

TOP: Trigonometric Ratios of Any Angle KEY: primary trigonometric ratios

12. ANS:

Use the sine law.

AC

sin65°=

46

sin68°

AC =46sin65°

sin68°

≈ 45.0

∠A = 180° − 65° + 68°( )

= 47°

Again, use the sine law.

BC

sin47°=

46

sin68°

BC =46sin47°

sin68°

≈ 36.3

The total amount of hedge needed is approximately 46 + 45.0 + 36.3, or 127.3 m.

PTS: 1 DIF: Average OBJ: Section 2.3 NAT: T 3

TOP: The Sine Law KEY: sine law

ID: A

3

13. ANS:

cos A =b

2+ c

2− a

2

2bc

=13.7( )

2+ 11.5( )

2− 5.5( )

2

2 13.7( ) 11.5( )

≈ 0.919359

∠A ≈ cos−1

0.919359

≈ 23.2°

∠A is approximately 23°.

PTS: 1 DIF: Average OBJ: Section 2.4 NAT: T 3

TOP: The Cosine Law KEY: cosine law | angle measure

14. ANS:

a) ∠A is in the second quadrant. Therefore, only the sine ratio is positive.

Use the Pythagorean theorem.

r2

= x2

+ y2

= −5( )2

+ 72

= 25 + 49

= 74

r = 74

Therefore, sinA =7

74, cos A = −

5

74, and tanA = −

7

5.

b) The quadrant in which the sine ratio is still positive, but the cosine and tangent ratios change from

negative to positive, is the first quadrant. In this quadrant, all three primary trigonometric ratios are

positive.

sinB =7

74, cos B =

5

74, and tanB =

7

5.

c) sinB =7

74

∠B ≈ 54°

Use the fact that ∠B is the reference angle for ∠A.

∠A = 180° − 54°

= 126°

PTS: 1 DIF: Average OBJ: Section 2.1 | Section 2.2

NAT: T 1 | T 2 TOP: Angles in Standard Position | Trigonometric Ratios of Any Angle

KEY: primary trigonometric ratios | reference angle

ID: A

4

15. ANS:

Draw a diagram.

Let x represent the distance that Leo is from the base of the monument.

tan41° =6

x

x =6

tan41°

Let ∠G represent the angle that Gursant would measure. The distance that Gursant is from the monument

is given by the expression 3.5 +6

tan41°.

tanG =6

3.5 +6

tan41°

∠G ≈ 30°

PTS: 1 DIF: Difficult OBJ: Section 2.2 NAT: T 3

TOP: Trigonometric Ratios of Any Angle KEY: tangent

ID: A

5

16. ANS:

a) This is the ambiguous case, so there are two triangles.

Triangle 1 Triangle 2

b) For triangle 1, For triangle 2,

sinB

b=

sinC

c

sin38°

7=

sinC

11

sinC =11sin38°

7

∠C ≈ 75.3°

∠C = 180° − 75.3°

≈ 104.7°

c) For triangle 1, For triangle 2,

∠A = 180° − 38° + 75.3°( )

= 66.7°

∠A = 180° − 38° + 104.7°( )

= 37.3°

d) For triangle 1, For triangle 2,

BC

sinA=

AC

sinB

BC

sin66.7°=

7

sin38°

BC =7sin66.7°

sin38°

≈ 10.4

BC

sinA=

AC

sinB

BC

sin37.3°=

7

sin38°

BC =7sin37.3°

sin38°

≈ 6.9

In triangle 1, the length of BC is 10.4 cm. In triangle 2, the length of BC is 6.9 cm.

PTS: 1 DIF: Average OBJ: Section 2.3 NAT: T 3

TOP: The Sine Law KEY: sine law | ambiguous case