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A ladder against a vertical wall makes an angle of 45º with the ground. The foot of the ladder is 3m from the wall. Find the length of the ladder - Mathematics

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Question

A ladder against a vertical wall makes an angle of 45º with the ground. The foot of the ladder is 3m from the wall. Find the length of the ladder

Solution

Let AB be the wall and CB, the ladder.

Then, AC = 3m and ∠ACB = 45º

`\text{Now, }\frac{CB}{AC}=\sec \text{45}^\text{o}=\sqrt{2}\Rightarrow \frac{CB}{3}=\sqrt{2}`

∴ Length of the ladder = CB = 3 √2

= (3 × 1.41) m = 4.23 m

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A ladder against a vertical wall makes an angle of 45º with the ground. The foot of the ladder is 3m from the wall. Find the length of the ladder Concept: Heights and Distances.
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