# A statue 1.6 m tall stands on the top of pedestal.

Question:

A statue 1.6 m tall stands on the top of pedestal. From a point on the ground, the angle of elevation of the top of the statue is 60° and from the same point the angle of elevation of the top of the pedestal is 45°. Find the height of the pedestal.

Solution:

Let be the pedestal of height m and  the statue of height  meter and angle of elevation at top of statue is 60° and angle of elevation of pedestal at the same point is 45°. Here we have to find height of pedestal.

The corresponding figure is here

$\Rightarrow \quad \tan 45^{\circ}=\frac{A B}{O A}$

$\Rightarrow \quad 1=\frac{h}{x}$

$\Rightarrow \quad x=h$

Again in $\triangle O A C$

$\Rightarrow \quad \tan 60^{\circ}=\frac{A C}{O A}$

$\Rightarrow \quad \sqrt{3}=\frac{h+1.6}{x}$

$\Rightarrow \quad \sqrt{3} x=h+1.6$

$\Rightarrow \quad h \sqrt{3}=h+1.6$

$\Rightarrow \quad h=\frac{1.6}{\sqrt{3}-1}$

$\Rightarrow \quad h=0.8(\sqrt{3}+1)$

Hence the height of pedestal is

$0.8(\sqrt{3}+1)$