Height and Distance problems
- 1. The angle of elevation of the top of a hill from each of the vertices A, B, C of a horizontal triangle is ?. The height of the hill is :
Options- A. b tan ? cosec B
- B. a tan ? cosec A 2
- C. c tan ? cosec C 2
- D. None of these Discuss
Correct Answer: a tan ? cosec A 2
Explanation:
- 2. A person standing on the bank of a river observes that the angle subtended by a tree on the opposite bank is 60°. When he retires 40 m from the bank, he finds the angle to be 30°. The breadth of the river is :
Options- A. 40 m
- B. 60 m
- C. 20 m
- D. 30 m Discuss
Correct Answer: 20 m
Explanation:
- 3. The angle of elevation of the top of an unfinished tower at a point distant 120 m from its base is 45°. If the elevation of the top at the same point is to be 60°, the tower must be raised to a height :
Options- A. 120 ( ?3 + 1 ) m
- B. 120 ( ?3 - 1 ) m
- C. 10 ( ?3 + 1 )
- D. None of these Discuss
Correct Answer: 120 ( ?3 - 1 ) m
Explanation:
- 4. The angle of elevation of the top of a tower at a point G on the ground is 30°. On walking 20 m towards the tower, the angle of elevation becomes 60°. The height of the tower is equal to :
Options- A. 10 m ?3
- B. 20 ?3 m
- C. 20 m ?3
- D. 10 ?3 m Discuss
Correct Answer: 10 ?3 m
Explanation:
- 5. From a point P on a level ground, the angle of elevation of the top of the tower is 30°. If the tower is 100 m high, the distance of the point P from the foot of the tower is :
Options- A. 100/ ?3 m
- B. 100 ?3 m
- C. 50?3 m
- D. 50/?3 m Discuss
Correct Answer: 100 ?3 m
Explanation:
- 6. A tower standing on a horizontal plane subtends a certain angle at a point 160 m apart from the foot of the tower. On advancing 100 m towards it, the tower is found to subtend an angle twice as before. The height of the tower is :
Options- A. 80 m
- B. 100 m
- C. 160 m
- D. 200 m Discuss
Correct Answer: 80 m
Explanation:
- 7. A man from the top of a 100 m high tower sees a car moving towards the tower at an angle of depression of 30°. After some time, the angle of depression becomes 60°. The distance (in m) traveled by the car during this time is :
Options- A. 100 ?3
- B. 200 ?3 3
- C. 100 ?3 3
- D. 200 ?3 Discuss
Correct Answer: 200 ?3 3
Explanation:
- 8.
sin A + sin A is ( 0° < A < 90° ) . 1 + cos A 1 - cos A
Options- A. 2 cosec A
- B. 2 sec A
- C. 2 sin A
- D. 2 cos A Discuss
Correct Answer: 2 cosec A
Explanation:
- 9. The angle of elevation of a ladder leaning against a wall is 60° and the foot of the ladder is 4.6 m away from the wall. The length of the ladder is
Options- A. 2.3 m
- B. 4.6 m
- C. 7.8 m
- D. 9.2 m Discuss
Correct Answer: 9.2 m
Explanation:
Let AB be the wall and BC be the ladder.
Then, ? ACB = 60° and AC = 4.6 m.
AC/BC = cos 60° = 1/2
BC = 2 x AC
= (2 x 4.6) m
= 9.2 m.
- 10. From the top of h meter high cliff the angles of depression of the top and the button of a tower are observed to be 30° and 60° respectively. The height of the tower is?
Options- A. h?3
- B. 2h?3
- C. h/3
- D. 2h/3 Discuss
Correct Answer: 2h/3
Explanation:
Let us draw a figure below as per given question.
Let AB = h meter be the height of cliff and CD = x meter be the height of the tower and also ? ADB = 60° and ?ACE = 30° ,
Now, from the figure, AE = (h - x) meter
From right triangle ABD, BD = h cot 60° = h/?3 m
From right triangle CEA. (h - x) = EC tan 30° = BD tan 30°
? h - x = h/?3 X 1/?3
? x = h - h/3 = 2h/3 meter
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