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.
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Answer 1

Explanation:

Height of the pedestal =2m

Let the height of the statue =hm

Angle of elevation of top of the statue =60

∘

Angke of elevation of top of the pedestal =45

∘

Let the distance between the point of observation and foot of the pedestal =xm

From the figure

tan45

∘

=

x

2

⇒1=

x

2

⇒x=2m

tan60

∘

=

x

2+h

⇒

3

=

2

2+h

[∵x=2m]

⇒2

3

⇒2+h⇒h=2

3

−2

⇒h=2(

3

−1)=2(1.732−1)

=2(0.732)=1.464m

∴ The height of the statue, h=1.454m

hope it helps you dear ❤❤