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?12 metres 5 metres 8 metres 10 metres

Solution

## The correct option is D 10 metres 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=(15−h) [∵ AC=15 and BC=h), BD=CE tan60∘=ACCE ⇒√3=15CE ⇒CE=15√3 …(1) tan30∘=ABBD 1√3=15−hBD 1√3=15−h15√3[∵ BD=CE and substituted the value of CE from (1)] ⇒(15−h)=1√3×15√3=153=5 ⇒h=15−5=10 m i.e., height of the electric pole = 10 m

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