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Question (11)

QN0036881

11. A building is observed from a point 30 m away at an angle of elevation of 30°. If the observer's eye is 1.6 m above the ground, the height of the building is:

(A) 10√3 m
(B) 10√3 + 1.6 m
(C) 30√3 + 1.6 m
(D) 15√3 m

Correct Answer: B

Explanation:

Height above eye level = 30 tan 30° = 10√3 m. Hence total height = 10√3 + 1.6 m.

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Question (12)

QN0036882

12. A ladder reaches a point 6 m above the ground when it makes an angle of 30° with the ground. The length of the ladder is:

(A) 3 m
(B) 6 m
(C) 12 m
(D) 6√3 m

Correct Answer: C

Explanation:

sin 30° = 6/L, so L = 12 m.

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Question (13)

QN0036883

13. A ladder 10 m long makes an angle of 60° with the ground. The height reached by the ladder is:

(A) 5 m
(B) 5√3 m
(C) 10√3 m
(D) 20 m

Correct Answer: B

Explanation:

Height = 10 sin 60° = 10 × √3/2 = 5√3 m.

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Question (14)

QN0036884

14. An 8 m ladder rests against a wall and makes an angle of 60° with the ground. The distance of its foot from the wall is:

(A) 4 m
(B) 4√3 m
(C) 8√3 m
(D) 6 m

Correct Answer: A

Explanation:

Horizontal distance = 8 cos 60° = 4 m.

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Question (15)

QN0036885

15. A ladder reaches the top of a wall of height 5√3 m and makes an angle of 60° with the ground. The length of the ladder is:

(A) 5 m
(B) 5√3 m
(C) 10 m
(D) 15 m

Correct Answer: C

Explanation:

sin 60° = 5√3/L, giving L = 10 m.

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Question (16)

QN0036886

16. A tree casts a shadow 10 m long when the angle of elevation of the Sun is 45°. The height of the tree is:

(A) 5 m
(B) 10 m
(C) 10√3 m
(D) 20 m

Correct Answer: B

Explanation:

Height = 10 tan 45° = 10 m.

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Question (17)

QN0036887

17. A tower casts a shadow 10√3 m long when the angle of elevation of the Sun is 30°. The height of the tower is:

(A) 5 m
(B) 10 m
(C) 20 m
(D) 30 m

Correct Answer: B

Explanation:

Height = 10√3 tan 30° = 10√3 × 1/√3 = 10 m.

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Question (18)

QN0036888

18. A 20 m high tower casts a shadow when the Sun's angle of elevation is 60°. The length of the shadow is:

(A) 20 m
(B) 20/√3 m
(C) 20√3 m
(D) 10√3 m

Correct Answer: B

Explanation:

tan 60° = 20/d, so d = 20/√3 m.

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Question (19)

QN0036889

19. A tower casts a shadow of length x when the Sun's angle of elevation is 60°. If the angle changes to 30°, the new shadow is:

(A) x/3
(B) 3x
(C) x√3
(D) x/√3

Correct Answer: B

Explanation:

Shadow is proportional to cot θ. Therefore, the ratio is cot 30°/cot 60° = 3, so the new shadow is 3x.

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Question (20)

QN0036890

20. A tower casts a 12 m shadow when the Sun's angle of elevation is 45°. What will be the shadow length when the angle becomes 60°?

(A) 6 m
(B) 4√3 m
(C) 6√3 m
(D) 12√3 m

Correct Answer: B

Explanation:

Tower height = 12 m. At 60°, shadow = 12/√3 = 4√3 m.

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Question (11)

11. A building is observed from a point 30 m away at an angle of elevation of 30°. If the observer's eye is 1.6 m above the ground, the height of the building is:

Explanation:

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Question (12)

12. A ladder reaches a point 6 m above the ground when it makes an angle of 30° with the ground. The length of the ladder is:

Explanation:

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Question (13)

13. A ladder 10 m long makes an angle of 60° with the ground. The height reached by the ladder is:

Explanation:

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Question (14)

14. An 8 m ladder rests against a wall and makes an angle of 60° with the ground. The distance of its foot from the wall is:

Explanation:

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Question (15)

15. A ladder reaches the top of a wall of height 5√3 m and makes an angle of 60° with the ground. The length of the ladder is:

Explanation:

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Question (16)

16. A tree casts a shadow 10 m long when the angle of elevation of the Sun is 45°. The height of the tree is:

Explanation:

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Question (17)

17. A tower casts a shadow 10√3 m long when the angle of elevation of the Sun is 30°. The height of the tower is:

Explanation:

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Question (18)

18. A 20 m high tower casts a shadow when the Sun's angle of elevation is 60°. The length of the shadow is:

Explanation:

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Question (19)

19. A tower casts a shadow of length x when the Sun's angle of elevation is 60°. If the angle changes to 30°, the new shadow is:

Explanation:

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Question (20)

20. A tower casts a 12 m shadow when the Sun's angle of elevation is 45°. What will be the shadow length when the angle becomes 60°?

Explanation:

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