Question

Determine the length of a ladder, if it is leaning against a vertical wall making an angle of inclination of ${30}^{\circ }$ with the ground and its foot is 15 m from the wall ?

• A. $15.77m$
• B. $10m$
• C. $10$$\sqrt{3}$ $m$
• D. $12.71$ $m$

Answer 1

The correct option is A $15.77m$

Let the ladder and wall form a triangle.

Here $AC$ is the ladder

from given, we have,

$\cos 30=\frac{BC}{AC}$

$\frac{\sqrt{3}}{2}=\frac{15}{AC}$

$AC=15\times \frac{2}{\sqrt{3}}$

$\therefore AC=17.32$

Hence the length of ladder.