Trigonometric Questions Answers

Trigonometric Ratios - Quant/Math - CAT 2008

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)

 

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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 = LTAO = 45^o
and angle of elevation from B = L TBO = 60^o
Distance between AB = AO + OB = x + y (say)
Now, in right triangle ATO,
tan 45^o =   OT/AO = 30/x
=> x = 30/ tan 45' = 30 m
and in right traingle BTO
tan 60^o =  OT/OB = 30/y
=> y =30  /  tan 60'  =  30  /  (3)^1/2  =  30(3)^1/2  /  3   = 17.32 m

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