Question

The foot of a ladder leaning against a wall of length $5$ meters rests on a level ground $5\sqrt{3}$ meters from the base of the wall. The angle of inclination of the ladder with the ground is

• A. ${60}^{\circ }$
• B. ${50}^{\circ }$
• C. ${40}^{\circ }$
• D. ${30}^{\circ }$

Answer 1

The correct option is D ${30}^{\circ }$

Consider $AB$ as the wall and $AC$ as the ladder, $BC$ being the ground
Now, In $△ABC$
$\therefore \tan \theta =\frac{AB}{BC}=\frac{5}{5\sqrt{3}}=\frac{1}{\sqrt{3}}$

$\therefore \theta ={30}^{\circ }$