Live Education Quiz

1

A ladder leans against a wall. The angle between the ladder and the ground is 60°. If the ladder is 10 m long, how high up the wall does it reach?

A

5√3 m

B

5 m

C

10√3 m

D

20 m

2

What is the bearing of West?

A

270°

B

180°

C

090°

D

360°

3

What is the angle of depression if a person looks down from a height to an object on the ground?

A

The angle between the line of sight and the horizontal

B

The angle between the vertical and the line of sight

C

The angle at the object

D

The angle at the observer's feet

4

If a point is at a bearing of 200°, in which quadrant is it?

A

Third quadrant (southwest)

B

Second quadrant (northwest)

C

Fourth quadrant (southeast)

D

First quadrant (northeast)

5

What is the value of cos 0°?

A

1

B

0

C

1/2

D

√3/2

6

What is the sector angle of a circle if the arc length is 10 cm and the radius is 5 cm?

A

2 radians

B

0.5 radians

C

50 radians

D

15 radians

7

A tower casts a shadow 20 m long when the sun's elevation is 30°. How tall is the tower?

A

20/√3 m

B

20√3 m

C

10 m

D

40 m

8

In a triangle, if tan θ = 4/3, what is sin θ?

A

4/5

B

3/5

C

5/4

D

3/4

9

Which of the following is a Pythagorean identity?

A

sin² θ + cos² θ = 1

B

tan² θ + 1 = sin² θ

C

1 + cot² θ = sec² θ

D

sin θ cos θ = 1

10

What is the value of sec 60°?

A

2

B

1/2

C

√3/2

D

2/√3

11

In a right-angled triangle, if the opposite side is 6 and the adjacent side is 8, what is tan θ?

A

3/4

B

4/3

C

3/5

D

5/4

12

If θ = 30°, what is the value of sin θ?

A

1/2

B

√3/2

C

1/√2

D

√3

13

From the top of a cliff 50 m high, the angle of depression of a boat is 30°. How far is the boat from the base of the cliff?

A

50√3 m

B

50/√3 m

C

100 m

D

25 m

14

What is the sector area of a circle with radius 6 cm and angle π/3 radians?

A

6π cm²

B

3π cm²

C

12π cm²

D

18π cm²

15

A ladder 13 m long reaches a window 12 m high. What is the angle of elevation of the ladder?

A

sin⁻¹(12/13)

B

cos⁻¹(12/13)

C

tan⁻¹(12/13)

D

tan⁻¹(13/12)

16

Simplify: 1 - sin² θ = ?

A

cos² θ

B

tan² θ

C

sec² θ

D

cot² θ

17

What is the reciprocal of sin θ?

A

cosec θ

B

sec θ

C

cot θ

D

cos θ

18

What is the angle between the line of sight and the horizontal when looking up called?

A

Angle of elevation

B

Angle of depression

C

Bearing

D

Sector angle

19

If a person observes an object at a bearing of 300°, what is the direction?

A

Northwest

B

Northeast

C

Southwest

D

Southeast

20

If the angle of depression from the top of a building to a car is 45° and the building is 30 m high, how far is the car from the building?

A

30 m

B

30√2 m

C

15 m

D

60 m

🎉 Practice Complete!