Trigonometric ratios - Quant/Math - CAT 2007
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 = 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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