Question

The angle of elevation from the point P on the ground to the top of a $10$ m high building is ${30}^o$. The angle of elevation from P to the top of a flag situated on the top of building is ${45}^o$. Find the height of flag.

Answer 1

$BC=10$ m

$\angle BPC={30}^{\circ }$

$\angle APC={45}^{\circ }$

$tan\left(\angle BPC\right)=\frac{BC}{PC}$

$\Rightarrow PC=10\sqrt{3}$ m

$tan\left(\angle APC\right)=\frac{AC}{PC}$

$\Rightarrow AC=10\sqrt{3}$ m

Height of flag $=AC-BC=10\sqrt{3}-10=10(\sqrt{3}-1)$ m