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- Question
- The height of a tower is 100 m. When the angle of elevation of the sun changes from 30° to 45°, the shadow of the tower becomes P meter smaller. The value of P is :
Options- A. 100 m
- B. 100 ?3 m
- C. 100( ?3 - 1) m
- D. 100 m ?3
- Correct Answer
- 100( ?3 - 1) m
Explanation
- 1. A tower stands at the end of a straight road. The angles of elevation of the top of the tower from two points on the road 500 m apart are 45° and 60°, respectively. Find out the height of the tower.
Options- A. 500 ?3 ?3 - 1
- B. 5000 ?3
- C. 500 ?3 ?3 + 1
- D. None of these Discuss
- 2. When the sun is 30° above the horizontal, the length of shadow cast by a building 50 m high is :
Options- A. 50 m ?3
- B. 50?3 m
- C. 25 m
- D. 25?3 m Discuss
- 3. The ratio of the length of a rod and its shadow is 1: ?3 .The angle of elevation of the sun is :
Options- A. 30°
- B. 45°
- C. 60°
- D. 90° Discuss
- 4. On the ground level the angle of elevation of the top of a tower is 30°, On moving 20 m nearer the tower, the angle of elevation found to be 60°. The height of the tower is?
Options- A. 10 m
- B. 10?3 m
- C. 15 m
- D. 20 m Discuss
- 5. The angle of elevation of the top of two vertical towers as seen from the middle point of the line joining the foot of the towers are 60° and 30° respectively. The ratio of the heights of the towers is?
Options- A. 2 : 1
- B. ?3 : 1
- C. 3 : 2
- D. 3 : 1 Discuss
- 6. From the top of a 25 m high, cliff the angle of elevation of a tower is found to be equal to the angle of depression of the foot of the tower. Find out the height of the tower.
Options- A. 40 m
- B. 48 m
- C. 50 m
- D. 52 m Discuss
- 7. The angle of elevation of the top of a tower from a point 20 m away from its base is 45°. The height of the tower is :
Options- A. 10 m
- B. 20 m
- C. 40 m
- D. 20 ?3 m Discuss
- 8. 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
- 9. 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
- 10. 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
Height and Distance problems
Search Results
Correct Answer: 500 ?3 ?3 - 1
Explanation:
Correct Answer: 50?3 m
Explanation:
Correct Answer: 30°
Explanation:
Correct Answer: 10?3 m
Explanation:
Let us draw a figure below from the given question.
Let AB = h meter be the height of the towers. B and C are two points such that BC = 20 m; ?ADB = 30° and ?ACB = 60° BC = x meter (let us assume)
Now, from right triangle ABC,
x = h cot 60°
? x = h/?3 meter
Again, from right triangle ABD,
h = (20 + x) tan 30°
put the value of x in above equation.
? x = h/?3
? h = (20 + h/?3) x 1/?3 ( ? tan 30° = 1/?3 )
? h - h/3 = 20/?3 ? 2h/3 = 20/?3
? h = 20 x 3/2?3 = 10?3 m
Correct Answer: 3 : 1
Explanation:
Let AB and CD be two towers of height h1 and h2 respectively and O the mid-point of the line joining the foots A and C of the towers.
Let OA = OC = x
Then h1 = x tan 60° = x?3
and h2 = x tan 30° = x/?3
? h1 /h2= 3/1.
Hence, h1 : h2 = 3 : 1
Correct Answer: 50 m
Explanation:
Correct Answer: 20 m
Explanation:
Correct Answer: a tan ? cosec A 2
Explanation:
Correct Answer: 20 m
Explanation:
Correct Answer: 120 ( ?3 - 1 ) m
Explanation:
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