The angle of elevation of the top of a building from the foot of the tower is $30°$ and the angle of elevation of the top of the tower from the foot of the building is $60°$. If the tower is $50$ m hi

Question

The angle of elevation of the top of a building from the foot of the tower is $30°$ and the angle of elevation of the top of the tower from the foot of the building is $60°$. If the tower is $50$ m high, then find the height of the building.

Accepted Answer

Step 1: Let $AB$ be the building and $XY$ be the tower ($= 50$ m). $	an 30° = \frac{AB}{AX}$ and $	an 60° = \frac{50}{AX}$.
Step 2: $\Rightarrow AB = \frac{1}{\sqrt{3}} 	imes AX$ and $AX = \frac{50}{\sqrt{3}}$
Step 3: $	herefore AB = \frac{1}{\sqrt{3}} 	imes \frac{50}{\sqrt{3}} = \frac{50}{3}$ m

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