Question

The ladder resting against a vertical wall is inclined at an angle of ${30}^{\circ }$ to the ground. The foot of the ladder is $7.5\text{m}$ from the wall. Find the length of the ladder.

• A. $8.66\text{m}$
• B. $7.66\text{m}$
• C. $10.66\text{m}$
• D. $9.66\text{m}$

Answer 1

The correct option is A $8.66\text{m}$

Let the length of the ladder be $l.$

In $△ABC,$
$\begin{array}{cc}\cos {30}^{\circ }& =\frac{7.5}{l}\\ \frac{\sqrt{3}}{2}& =\frac{7.5}{l}\\ l& =\frac{15}{\sqrt{3}}\\ & =5\sqrt{3}\\ & \approx 8.66\text{m}\end{array}$

Hence, the length of the ladder is $8.66\text{m}.$