Trigonometric ratios  Quant/Math  CAT 2016
Question 4 the day:
July 02, 2002
The question for the day is a quant problem from the topic of Trigonometric ratios.
Question:
 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 choice (3). Correct Answer  47.32
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 = 45^{o}
and angle of elevation from B = TBO = 60^{o}
Distance between AB = AO + OB = x + y (say)
Now, in right triangle ATO,
tan 45^{o} =
=> x = = 30 m
and in right traingle BTO
tan 60^{o} =
=> y = = 17.32 m
Hence, the required distance = x + y = 30 + 17.32 = 47.32 m
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