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Question
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° with the horizontal.
∴ΔABC is a 30°-60°-90°, 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 `sqrt18.75~~4.33m`
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