Two buildings are in front of each other on a road of width 15 meters. From the top of the first building, having a height of 12 meter, the angle of elevation of the top of the second building is 30°.What is the height of the second building?

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#### Solution

Let AB and CD be the two building standing on the road.

Suppose the height of the second building be h m.

Here, AB = 12 m, BD = 15 m, ∠CAE = 30º and AE ⊥ CD.

CE = CD − ED = (h − 12) m (ED = AB)

AE = BD = 15 m

In right ∆AEC,

\[\tan30^\circ = \frac{CE}{AE}\]

\[ \Rightarrow \frac{1}{\sqrt{3}} = \frac{h - 12}{15}\]

\[ \Rightarrow h - 12 = \frac{15}{\sqrt{3}} = 5\sqrt{3}\]

\[ \Rightarrow h = \left( 12 + 5\sqrt{3} \right) m\]

Thus, the height of the second building is

\[\left( 12 + 5\sqrt{3} \right)\] m.

Concept: Heights and Distances

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