Question : A 22 m long ladder (whose foot is on the ground) leans against a wall making an angle of 60° with the wall. What is the height (in m) of the point where the ladder touches the wall from the ground?
Option 1: $\frac{22 \sqrt{2}}{3}$
Option 2: $11 \sqrt{2}$
Option 3: $11$
Option 4: $11 \sqrt{3}$
Correct Answer: $11 \sqrt{3}$
Solution :
Given,
In $\triangle$ABC
AB is the height of the point of the ladder on the wall.
$\sin 60° = \frac{\text{AB}}{\text{AC}}$
⇒ $\frac{\sqrt{3}}{2} = \frac{\text{AB}}{22}$
⇒ AB = $11\sqrt{3}$ m
Hence, the correct answer is $11\sqrt{3}$.
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