Question

From a point on the ground, the angles of elevation of the bottom and the top of a tower fixed at the top of a 20 m high building are $45°$ and $60°$ respectively. Find the height of the tower.

Solution

1

Tower of height h m on building of 20 m, angles 45° and 60° from point D

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2

In right $△BCD$: $\tan 45°=\frac{BC}{CD}\Rightarrow 1=\frac{20}{CD}\Rightarrow CD=20$ m

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3

In right $△ACD$: $\tan 60°=\frac{AC}{CD}\Rightarrow \sqrt{3}=\frac{20+h}{20}$

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4

$h=20(\sqrt{3}-1)$ m

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