Q. 25.0( 3 Votes )

A ladder is placed against a wall such that it just reaches the top of thewall. The foot of the ladder is 1.5 m away from the wall and the ladder isinclined at an angle of 60^{ o}with the ground. Findthe height of the wall.

Answer :

Given:

Distance of the ladder from the wall, d = BC = 1.5 m

Angle of elevation, θ = 60°

To find: Height of the wall, h:

Solution:

Let AC be the ladder and B be the foot of the wall.

In right angled Δ ABC,

tan [θ] = Opposite / Adjacent

Here θ = 60°

And also the opposite side is AB and the adjacent side is BC

∴ tan 60 ^{ o } = AB/BC

tan 60 ^{ o } = AB/BC

AB = BC tan 60 ^{ o }

We know that BC = 1.5m

= 1.5 × (√ 3)

= 1.5 × 1.732

= 2.598 m

Therefore the height of the wall is 2.598 m.

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