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A ladder 14 m long rests against a wall. If the foot of ladder is 7 m from the wall, then the angle of elevation is

  1. 15°

  2. 30°

  3. 45°

  4. 60°

Heights & Distances

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Answer

Let AB be the ladder and θ be the angle of elevation.

A ladder 14 m long rests against a wall. If the foot of ladder is 7 m from the wall, then the angle of elevation is. Heights and Distances, ML Aggarwal Understanding Mathematics Solutions ICSE Class 10.

Considering right angled △ABC we get,

cos θ=714cos θ=12cos θ=cos 60°θ=60°.\Rightarrow \text{cos θ} = \dfrac{7}{14} \\[1em] \Rightarrow \text{cos θ} = \dfrac{1}{2} \\[1em] \Rightarrow \text{cos θ} = \text{cos 60°} \\[1em] \Rightarrow θ = 60°.

Hence, Option 4 is the correct option.

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