Question

In figure,a tower AB is 20 m high and BC,its shadow in the ground,is $20\sqrt{3}$ m long. Find the sun's altitude.

Answer 1

Given,AB is the tower and BC is its shadow.

$\therefore tan\theta =\frac{AB}{BC}$

$[\because tan\theta =\frac{\text{POpposite~side}}{\text{Adjacent~side}}]$

$\Rightarrow tan\theta =\frac{20}{20\sqrt{3}}=\frac{1}{\sqrt{3}}$

$\Rightarrow tan\theta =tan{30}^{\circ }[\because tan{30}^{\circ }=\frac{1}{\sqrt{3}}]$

$\Rightarrow \theta ={30}^{\circ }$