Question

A $20\text{m}$ long ladder rests against a wall. If the foot of the ladder is $10\text{m}$ from the wall, what is the angle of elevation?

• A. $\frac{\pi }{6}$
• B. $\frac{\pi }{4}$
• C. $\frac{\pi }{3}$
• D. $\frac{\pi }{2}$

Answer 1

Answer: (C)

$\frac{\pi }{3}$

Let $AC$ be the ladder and $AB$ be the wall,

$\therefore AC=20\text{m}$

$BC=10\text{m},$ distance of the foot of the ladder from the wall.

Let $\angle ACB=\theta$.

In $△ACB,$

$\Rightarrow \cos \theta =\frac{BC}{AC}=\frac{10}{20}=\frac{1}{2}$

$\Rightarrow \cos \theta =\frac{1}{2}$

$\Rightarrow \cos \theta =\cos 60°$

$\Rightarrow \theta =60°=\frac{\pi }{3}$

Hence, the answer is $\frac{\pi }{3}.$