A ladder makes 60° with ground when it leans against the wall. The ladder slides down by 5 m along the ground making the angle 45°. Find the length of the ladder.
Explanation:
Let the length of the ladder be x, i.e., AC = DE = x.
In ∆ABC, cos60° = 1/2 = AB/AC
⇒ AB = AC/2 …(1)
In ∆DBE, cos45° = 1/√2 = DB/DE
⇒ DB = DE/√2 …(2)
We know, DB – AB = 5.
From (1) and (2)
DE/√2 – AC/2 = 5
⇒ x/√2 – x/2 = 5
⇒ (√2 - 1)x/2 = 5
⇒ x = 10/(√2 - 1) = 10(√2 + 1).
Hence, option (d).
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