Question

A statue 1.6m tall,stands on the top of a 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 top of elevation of the top of the pedestal is 45°. Find the height of the pedestal?

Answer 1

Let AB be the height of statue .

D is the point on the ground from where the elevation is taken .

Height of pedestal $= BC = AC - AB$

As per question ,

In right triangle BCD ,

$tan45° = \frac {BC}{CD}$

$\implies 1 = \frac {BC}{CD}$

$\implies BC = CD$

Also ,

In right triangle ACD ,

$tan60° = \frac {AC}{CD}$

$\implies \sqrt{3} = \frac {AB+ BC}{CD}$

$\implies \sqrt{3} CD = 1.6m + BC$

$\implies \sqrt{3} BC = 1.6m + BC$

$\implies \sqrt{3} BC - BC = 1.6m$

$\implies BC(\sqrt{3}-1) = 1.6m$

$\implies BC = \frac {1.6}{(\sqrt{3}-1)} m$

$\implies BC = 0.8 (\sqrt{3}+1) m$

Thus , the height of the pedestal is $0.8(\sqrt{3} +1)$ m .