Question

# The top of a $$15$$ metre high tower makes an angle of elevation of $$\displaystyle 60^{0}$$ with the bottom of an electric pole and angle of elevation of $$\displaystyle 30^{0}$$ with the top of the pole. What is the height of the electric pole?

A
5 metres
B
8 metres
C
10 metres
D
12 metres

Solution

## The correct option is C $$10$$ metresLet $$AB$$ be the tower and $$CD$$ be the electric poleThen $$\displaystyle \angle ACB=60^{0},\angle EDB=30^{0}$$ and $$\displaystyle AB=15$$ mLet $$\displaystyle CD=h.$$ Then $$\displaystyle BE=\left ( AB-AE \right )$$$$\displaystyle =\left ( AB-CD \right )=\left ( 15-h \right )$$We have $$\displaystyle \frac{AB}{AC}=\tan 60^{0}=\sqrt{3}$$$$\displaystyle \Rightarrow AC=\frac{AB}{\sqrt{3}}=\frac{15}{\sqrt{3}}$$And $$\displaystyle \frac{BE}{DE}=\tan 30^{0}=\frac{1}{\sqrt{3}}$$$$\displaystyle \Rightarrow DE=\left ( BE\times \sqrt{3} \right )$$ $$\displaystyle =\sqrt{3}\left ( 15-h \right )$$$$\displaystyle \Rightarrow 3h=\left ( 45-15 \right )$$$$\Rightarrow h=10$$ mMathematics

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