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Trigonometric Ratios - Quant/Math - CAT 2013

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Question 4 the day: July 2, 2002
The angle of elevation of the top of a tower 30 m high, from two points on the level ground on its opposite sides are 45 degrees and 60 degrees. What is the distance between the two points?
(1) 30   (2) 51.96   (3) 47.32   (4) 81.96
Correct Answer - (3)

Solution:

Let OT be te tower.

Therefore, Height of tower = OT = 30 m
Let A and B be the two points on the level ground on the opposite side of tower OT.

Then,
angle of elevation from A = TAO = 45o
and angle of elevation from B = TBO = 60o
Distance between AB = AO + OB = x + y (say)
Now, in right triangle ATO,
tan 45o =
=> x = = 30 m
and in right traingle BTO
tan 60o =
=> y = = 17.32 m

Hence, the required distance = x + y = 30 + 17.32 = 47.32 m
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