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A man of height 1 .5 m sees the top of a tree and the angle of elevation of the top at his eye is $60 °$ . If the distance of the man from the tree is 36 m then what will be the height of the tree?

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63m

63.74m

62.90m

63.85m

answer is D.

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Detailed Solution

Given,
The height of the man =

1.5

m.
The distance of the man from the tree =

36

m.
The angle

θ = 60 °

We draw the diagram,
Question Image

We have,

D E = 36 m B C = 36 m B D = 1.5 m C E = 1.5 m

Using the identity

tan θ = Perpendicular Base

Δ A B C

tan θ = AC BC

Substituting BC=36 and

θ

60 °

in the equation

tan θ = AC BC

⇒ tan 60 ° = A C 36 ⇒ A C = 36 tan 60 ° ⇒ A C = 36 × 3 [∵ tan 60 ° = 3] ⇒ A C = 62.35 m

The height of the tree,

h = A C + C E ⇒ h = 62.35 + 1.5 ⇒ h = 63.85 m

Thus the height of the tree will be

63.85

m.
Therefore the correct option is 4.

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