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A ladder makes 45° with the ground when it leans against a wall. The ladder slides down by 4 m along the wall and finally makes an angle of 30° with the ground. Find the length of the ladder.

A ladder makes 45° with the ground when it leans against a wall. The ladder slides down by 4 m along the wall and finally makes an angle of 30° with the ground. Find the length of the ladder. Correct Answer 4√2(2 + √2)

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According to given data,

AC = DE = ladder length

BE = AB – 4

In ΔABC,

Sin45° = AB/AC

AC = AB√2

Now in ΔBED,

Sin30° = BE/ED

DE = 2BE

Substitute, BE = AB – 4 and DE = AC = AB√2

AB√2 = 2(AB – 4)

⇒ AB = 4(2 + √2)

∴ AC = 4√2(2 + √2)

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