Question

A statue 1.6 m tall stands on the top of pedestal. From a point on the 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.

Answer 1

In $\Delta BCD$

$\tan {30}^o=\frac{BC}{CD}$

$\frac{1}{\sqrt{3}}=\frac{h}{CD}$

$CD=\sqrt{3}h$m ........$\left(1\right)$

Now,

In $\Delta ACD$

$\tan {60}^o=\frac{AC}{CD}$

$=\frac{AB+BC}{CD}$

From equation $\left(1\right)$ substitution value of CD

$\tan {60}^o=\frac{1.6+h}{\sqrt{3}h}$

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

$\Rightarrow 3h-h=1.6$

$2h=1.6$

$h=0.8$m

Height of Pedestal.