An observer 1.6 m tall is 20?3 away from a tower. The angle of elevation from hi

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Question
An observer 1.6 m tall is 20√3 away from a tower. The angle of elevation from his eye to the top of the tower is 30�. The heights of the tower is:
Options
A. 21.6 m
B. 23.2 m
C. 24.72 m
D. None of these

Correct Answer

21.6 m

Explanation
Let AB be the observer and CD be the tower.

Draw BE ⊥ CD.

Then, CE = AB = 1.6 m,

BE = AC = 20√3 m.

DE	= tan 30� =	1
BE	= tan 30� =	√3

⟹ DE =	20√3	m = 20 m.
	√3

∴ CD = CE + DE = (1.6 + 20) m = 21.6 m.

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Height and Distance problems

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1. 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

2. A man standing at a point P is watching the top of a tower, which makes an angle of elevation of 30� with the man's eye. The man walks some distance towards the tower to watch its top and the angle of the elevation becomes 60�. What is the distance between the base of the tower and the point P?
Options
A. 4√3 units
B. 8 units
C. 12 units
D. Data inadequate
E. None of these

3. A train overtakes two persons walking along a railway track. The first one walks at 4.5 km/hr. The other one walks at 5.4 km/hr. The train needs 8.4 and 8.5 seconds respectively to overtake them. What is the speed of the train if both the persons are walking in the same direction as the train?
Options
A. 66 km/hr
B. 72 km/hr
C. 78 km/hr
D. 81 km/hr

4. A train 108 m long moving at a speed of 50 km/hr crosses a train 112 m long coming from opposite direction in 6 seconds. The speed of the second train is:
Options
A. 48 km/hr
B. 54 km/hr
C. 66 km/hr
D. 82 km/hr

5. Two trains, each 100 m long, moving in opposite directions, cross each other in 8 seconds. If one is moving twice as fast the other, then the speed of the faster train is:
Options
A. 30 km/hr
B. 45 km/hr
C. 60 km/hr
D. 75 km/hr

6. From a point P on a level ground, the angle of elevation of the top tower is 30�. If the tower is 100 m high, the distance of point P from the foot of the tower is:
Options
A. 149 m
B. 156 m
C. 173 m
D. 200 m

7. The angle of elevation of the sun, when the length of the shadow of a tree √3 times the height of the tree, is:
Options
A. 30�
B. 45�
C. 60�
D. 90�

8. Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 30� and 45� respectively. If the lighthouse is 100 m high, the distance between the two ships is:
Options
A. 173 m
B. 200 m
C. 273 m
D. 300 m

9. A sum of Rs. 12,500 amounts to Rs. 15,500 in 4 years at the rate of simple interest. What is the rate of interest?
Options
A. 3%
B. 4%
C. 5%
D. 6%
E. None of these

10. Reena took a loan of Rs. 1200 with simple interest for as many years as the rate of interest. If she paid Rs. 432 as interest at the end of the loan period, what was the rate of interest?
Options
A. 3.6
B. 6
C. 18
D. Cannot be determined
E. None of these

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