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.
(AS)​

Answer 1

Answer:

• Height of statue is 2(√3 - 1) m.

Step-by-step explanation:

Given :

• Height of pedestal is 2 m .
• Angle of elevation of the top of statue is 60°.
• Angle of elevation of the top of pedestal is 45°.

To find :

• Height of statue.

Solution :

Let, Height of pedestal be BD, height of statue be AD, angle of elevation of top of statue be ∠BCA and angle of elevation of top of pedestal be ∠BCD.

So,

In ∆DBC :

$\sf \longrightarrow tan \: 45\degree = \dfrac{DB}{BC}$

• tan 45° = 1 and DB is 2 m.

$\sf \longrightarrow 1 = \dfrac{2}{BC}$

$\longrightarrow \pmb{\sf BC = 2}$

Value of BC is 2 m.

Now,

In ∆ABC :

$\sf \longrightarrow tan \: 60\degree = \dfrac{AB}{BC}$

• tan 60° = √3 and we can write AB = AD + BD.

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

• BD = 2 m and BC is also 2 m.

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

$\sf \longrightarrow 2\sqrt{3} = AD + 2$

$\sf \longrightarrow 2\sqrt{3} - 2 = AD$

$\longrightarrow \pmb{\sf AD = 2(\sqrt{3} - 1)}$

AD is Height of statue.

∴ Height of statue is 2(√3 - 1) m.

Answer 2

Answer:

Given :-

• 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°.

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,

$\longmapato$ 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 :

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

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

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

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

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