Question

The top of a tower is observed from two points in the same horizontal line through a point on the base of the4 tower. If the angles of elevation at the two points which are on the same side of the tower are ${30}^o$ and${45}^o$ and the distance between them is $60m$, find the height of the tower.

Answer 1

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Let $OB=x$

$\therefore tan{45}^{\circ }=\frac{h}{x}=1$ ; $h=x$

$\therefore CO=h+60$

$\therefore tan{30}^{\circ }=\frac{h}{h+{60}^{\circ }}$

$\therefore \frac{1}{\sqrt{3}}=\frac{h}{h+{60}^{\circ }}$

$\therefore \sqrt{3}h=h+{60}^{\circ }$

$\therefore h=\left(\frac{60}{\sqrt{3}-1}\right)m$

$\therefore h=30(\sqrt{3}+1)m$