Height and Distance problems
- 1. At a point, 15 m away from the base of a 15 m high house, the angle of elevation of the top is :
Options- A. 45°
- B. 30°
- C. 60°
- D. 90° Discuss
Correct Answer: 45°
Explanation:
- 2. A tower subtends an angle of 30° at a point on the same level as the foot of the tower. At a second point, h m above the first, the depression of the foot of the tower is 60°. The horizontal distance of the tower from the point is :
Options- A. h cot 60°
- B. h cot 30°
- C. h cot 60° 2
- D. h cot 30° 2 Discuss
Correct Answer: h cot 60°
Explanation:
- 3. The angle of elevation of the sun when the length of the shadow of a pole is ?3 times the height of the pole will be :
Options- A. 30°
- B. 60°
- C. 90°
- D. 45° Discuss
Correct Answer: 30°
Explanation:
- 4. The tops of two poles of height 20 m and 14 m are connected by a wire. If the wire makes an angle 30° with the horizontal, then the length of the wire is :
Options- A. 12 m
- B. 10 m
- C. 8 m
- D. None of these Discuss
Correct Answer: 12 m
Explanation:
- 5. The top of a 15 m high tower makes an angle of elevation of 60° with the bottom of an electric pole and an angle of elevation of 30° with the top of the pole. What is the height of the electric pole?
Options- A. 5 m
- B. 8 m
- C. 10 m
- D. 12 m Discuss
Correct Answer: 10 m
Explanation:
- 6. From a 15 m high bridge on the river, the angle of depression of a boat is 30°. If the speed of the boat be 6 Km/h, then the time taken by the boat to reach exactly below the bridge will be :
Options- A. 9 ?3 second
- B. 19 / ?3 second
- C. 3 ?3 second
- D. None of these Discuss
Correct Answer: 9 ?3 second
Explanation:
- 7. The angle of elevation of a tower from a distance 50 m from its foot is 30°. The height of the tower is :
Options- A. 50 ?3 m
- B. 50 m ?3
- C. 75 ?3 m
- D. 75 m ?3 Discuss
Correct Answer: 50 m ?3
Explanation:
- 8. If r sin ? = 1, r cos ? = ? 3 then the value of ( ? 3 tan ? + 1 ) is :
Options- A. ?3
- B. 1 ?3
- C. 1
- D. 2 Discuss
Correct Answer: 2
Explanation:
- 9. Two posts are x meter apart and the height of one is double that of the other. If from the midpoint of the line joining their feet, an observer finds the angular elevations of their tops to be complementary, then the height (in meter) of the shorter post is :
Options- A. x 2 ?2
- B. x 4
- C. x ?2
- D. x ?2 Discuss
Correct Answer: x 2 ?2
Explanation:
- 10. The angles of depression of two ships from the top of a light house are 45° and 30° towards east. if the ships are 200 m apart, find the height of the light house .
Options- A. 100 m
- B. 173 m
- C. 200 m
- D. 273 m Discuss
Correct Answer: 273 m
Explanation:
Let us draw a figure below as per given question.
Let AB = h meter be the height of the tower and two ships are situated at D and C respectively; such that, CD = 200 m; ?ADC = 30° ?ACB = 45° and BC = x meter (say)
Now from right triangle ABC,
tan 45° = h/x ? 1 = h/x
? x = h
Again from right triangle ABD,
tan 30° = h/( 200 + x )
? 1/?3 = h/( 200 + x )
Since x = h , we will get.
? 1/?3 = h/(200 + h )
? (200 + h ) = h X ?3
? h X ?3 - h = 200
? h x 1.732 - h = 200
? h(1.732 - 1) = 200
? h = 200/0.732 = 273.2 m = 273 m
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