Question

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

Answer 1

Let DC be the tower and BC be the building. Then,

$\angle CAB={45}^o,\angle DAB={60}^o,BC=20m$

Let height of the tower, $DC=hm$.

In right $△ABC$,

$\tan {45}^o=\frac{BC}{AB}$

$1=\frac{20}{AB}$

$AB=20m$

In right $△ABD$,

$\tan {60}^o=\frac{BD}{AB}$

$\sqrt{3}=\frac{h+20}{20}$

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