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A ladder is placed against a vertical wall such that it just reaches the top of the wall. The foot of the ladder is 1.5 m away from the wall and the ladder is inclined at an angle of $60 °$ with the ground. What will be the height of the wall?

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1.4 3

1.5 2

1.5 5

1.5 3

answer is D.

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Detailed Solution

Given that,
The distance between the foot of the ladder and the wall= 1.5 m therefore

B C = 1.5

m . The ladder is inclined at an angle =

60 °

therefore

θ = 60 °

.
Considering, the right angle triangle ABC,
Question Image

We apply the tangent rule in the right angle triangle

Δ A B C

tan θ = height Base ⇒ tan θ = h B C

Substituting

θ

60 °

and BC=1.5 in

tan θ = h B C

⇒ tan 60 ∘ = h 1.5 ⇒ h = 1.5 × 3 [∵ tan 60 ∘ = 3] ⇒ h = 1.5 3

Thus the height of wall will be

1.5 3

m.
Therefore the correct option is 4.

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