Question

from a point on the ground the angle of elevation of the bottom and the top a transmission tower fixed at the top of a 20m high building are 45 degree and 60 degree respectively. Find the height of the tower.​

Answer 1

EXPLANATION.

Let us assume that BC = building.

Let us assume that AB = transmission tower.

D be the point on the ground from elevation

angle to be measured.

$\sf : \implies \: in \: \triangle \: bcd \\ \\ \sf : \implies \: \tan( \theta) = \frac{perpendicular}{base} \\ \\ \sf : \implies \: \tan(45 \degree) = \frac{bc}{cd} \\ \\ \sf : \implies \: 1 = \frac{20}{cd} \\ \\\sf : \implies \: cd \: = 20 \: cm$

$\sf : \implies \: in \: \triangle \: acd \\ \\ \sf : \implies \: \tan(60 \degree) \: = \frac{ac}{cd} \\ \\ \sf : \implies \: \tan(60 \degree) \: = \frac{ab + bc}{cd} \\ \\ \sf : \implies \: \sqrt{3} = \frac{ab \: + 20}{20} \\ \\ \sf : \implies \: ab \: = (20 \sqrt{3} - 20)m \\ \\ \sf : \implies \: ab \: = 20( \sqrt{3} - 1)m$

$\sf : \implies \: \orange{ \underline{height \: of \: tower \: = 20( \sqrt{3} - 1)m }}$