A ladder leaning against a wall makes an angle of 60° with the horizontal. If the foot of the ladder is 2.5 m away from the wall, find the length of the ladder.

Solution

Let AB be the ladder and CA be the wall.

The ladder makes an angle of 60^o with the horizontal.
∴ ΔABC is a 30^o-60^o-90^o, right triangle.

Given: BC = 2.5 m, ∠ABC = 60°
AB = 5 cm and ∠BAC = 30°

From Pythagoras Theorem, we have
AB² = BC² + CA²
5² = (2.5)² + (CA)²
(CA)² = 25 – 6.25 = 18.75 m
Hence, length of the ladder is $square root of 18.75 end root space almost equal to 4.33 straight m$

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Circles

A ladder leaning against a wall makes an angle of 60° with the horizontal. If the foot of the ladder is 2.5 m away from the wall, find the length of the ladder.

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