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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
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B
8 metres
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C
10 metres
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D
12 metres
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Solution

The correct option is C $$10$$ metres
Let $$AB$$ be the tower and $$CD$$ be the electric pole
Then $$\displaystyle \angle ACB=60^{0},\angle EDB=30^{0}$$ and $$\displaystyle AB=15$$ m
Let $$\displaystyle CD=h.$$ 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 $$\displaystyle \frac{BE}{DE}=\tan 30^{0}=\frac{1}{\sqrt{3}}$$
$$\displaystyle \Rightarrow DE=\left ( BE\times \sqrt{3} \right )$$ $$\displaystyle =\sqrt{3}\left ( 15-h \right )$$
$$\displaystyle \Rightarrow 3h=\left ( 45-15 \right )$$
$$\Rightarrow h=10$$ m

640493_374557_ans_ae761e7aa76e486a932810b9615b3d93.png

Mathematics

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