Question

A ladder leaning against a vertical wall, makes an angle of ${60}^{\circ }$ with the ground. The foot of the ladder is $3.5$m away from the wall. Find the length of the ladder.

Answer 1

Let $AC$ denote the ladder and $B$ be foot of the wall.

Let the length of the ladder $AC$ be $x$ metres.

Given that $\angle CAB={60}^{\circ }$ and $AB=3.5$m

In the right $△CAB,\cos {60}^{\circ }=\frac{AB}{AC}$

$\Rightarrow AC=\frac{AB}{\cos {60}^{\circ }}$

$\therefore x=2\times 3.5=7$m

Thus, the length of the ladder is $7$m.