Height and Distance problems
- 1. A vertical pole is 75m high. Find the angle subtended by the pole a point 75 m away from its base.
Options- A. 30°
- B. 45°
- C. 60°
- D. 90° Discuss
Correct Answer: 45°
Explanation:
Let us draw a figure below as per given question.
Let AB = 75 m be the height of pole and C is a point on the ground such that BC = 75m
Now, from right triangle ABC.
tan ? = AB/BC = 75/75
? tan? = 1
? ? = 45°
- 2. A person standing on the bank of river finds that the angle of elevation of the top of a tower on opposite side bank is 45°. Which of the following statement is correct
Options- A. Breadth of the river is half of the height of the tower
- B. Breadth of the river and the height of the tower are equal
- C. Breadth of the river is twice the height of the tower
- D. None of these Discuss
Correct Answer: Breadth of the river and the height of the tower are equal
Explanation:
Let us draw a figure below as per given question.
Let AB = h m be the height of the tower, BC = x m be the breadth of the river and also ?ACB = 45°
Now from right triangle ABC
tan 45° = h/x ? 1 = h/x
? x = h
Hence, breadth of the river = height of the tower
- 3. 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
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
- 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
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
- 5. 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
Correct Answer: 30°
Explanation:
- 6. 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
Correct Answer: 50?3 m
Explanation:
- 7. 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
Correct Answer: 500 ?3 ?3 - 1
Explanation:
- 8. 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 Discuss
Correct Answer: 100( ?3 - 1) m
Explanation:
- 9. 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
Correct Answer: 50 m
Explanation:
- 10. 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
Correct Answer: 20 m
Explanation:
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