Question

A statue stands on the top of a 2 m tall 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 statue.​

Answer 1

$\large\sf\bullet{\pink{\underline{Answer}}}$

$\small\sf{\bullet{\red{Here}}}$

Given :-

Height of pedestal = 2m

Angle of elevation off the top of statue = 60°

Angle of elevation off the top of pedestal = 45°

To Find :-

What is the height of the statue.

Solution :-

Let,

$\mapsto$ Height of the statue = AD

$\mapsto$ Height of the pedestal = BD

$\longmapsto$ In ∆DBC :

$\implies \sf tan 45^{\circ} =\: \dfrac{DB}{BD}$

As we know that, [ tan 45° = 1 ]

$\implies \sf 1 =\: \dfrac{2}{BC}$

By doing cross multiplication we get :

$\implies \sf BC =\: 2(1)$

$\sf\bold{\pink{BC =\: 2\: m}}$

Again,

In ∆ABC :

$\implies \sf tan 60^{\circ} =\: \dfrac{AB}{BC}$

As we know that, [ tan 60° = √3 ]

$\implies \sf \sqrt{3} =\: \dfrac{AD + BD}{BC}$

Given :

BC = 2 m

$\implies \sf \sqrt{3} =\: \dfrac{AD + 2}{2}$

By doing cross multiplication we get :

$\implies \sf AD + 2 =\: 2\sqrt{3}$

$\implies \sf AD =\: 2(\sqrt{3} - 2)$

$\implies \sf AD =\: 2(\sqrt{3} - 1)$

$\implies \sf\bold{{AD =\: 2(\sqrt{3} - 1)\: m}}$

$\sf\boxed{\bold{\red{The\: height\: of\: the\: statue\: is\: 2(\sqrt{3} - 1)\: m.}}}$

Answer 2

Answer:

1.454 m

Explanation:

Refer to attachment

Hope it helps