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Question

The top of a 15m high tower makes an angle of depression of 60 with the bottom of an electric pole and angle of depression of 30 with the top of the pole. What is the height of the electric pole?


  1. 12 metres

  2. 5 metres

  3. 8 metres

  4. 10 metres


Solution

The correct option is D

10 metres


Quantitative Aptitude: Height and Distance
Consider the diagram shown above. AC represents the tower and DE represents the pole.
Given that AC=15 m, ADB=30, AEC=60.
Let DE=h
Then, BC=DE=h,
AB=(15h) [ AC=15 and BC=h),
BD=CE
tan60=ACCE
3=15CE
CE=153 (1)
tan30=ABBD
13=15hBD
13=15h153[ BD=CE and substituted the value of CE from (1)]
(15h)=13×153=153=5
h=155=10 m
i.e., height of the electric pole = 10 m

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