Question

A statue, 2 m 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
angle of elevation of the
top of the pedestal
is 45°. Find the height of
the pedestal​

Answer 1

Step-by-step explanation:

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Answer 2

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.