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# From the top of a building 30 m high, the top and bottom of a tower are observed to have angles of depression 30º and 45º respectively. Find the height of the tower - CBSE Class 10 - Mathematics

#### Question

From the top of a building 30 m high, the top and bottom of a tower are observed to have angles of depression 30º and 45º respectively. Find the height of the tower

#### Solution

Let AB be the building and CD be the tower.

Then, AB = 30 m. Let DC = x.

Draw DE ⊥ AB. Then AE = CD = x.

∴ BE = (30 – x) m.

\text{Now, }\frac{AC}{AB}=\text{cot 45}^\text{o}=1

\Rightarrow \frac{AC}{30}=1\Rightarrow AC=30 m

∴ DE = AC = 30 m.

\frac{BE}{DE}=\text{tan }30^\text{o}=\frac{1}{\sqrt{3}}

\Rightarrow\frac{BE}{30}=\frac{1}{\sqrt{3}}

\Rightarrow BE=\frac{30}{\sqrt{3}}

\therefore CD=AE=AB-BE=( 30-\frac{30}{\sqrt{3}} )

=30( 1-\frac{1}{\sqrt{3}})m

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Solution From the top of a building 30 m high, the top and bottom of a tower are observed to have angles of depression 30º and 45º respectively. Find the height of the tower Concept: Heights and Distances.
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