Question

A ladder $20m$ long is placed against a vertical wall of height $10$ metres. Find the distance between the foot of the ladder and the wall and also the inclination of the ladder to the horizontal.

• A. $17.32m$; $\theta ={30}^o$
• B. $17.32m$; $\theta ={60}^o$
• C. $17.32m$; $\theta ={45}^o$
• D. $27.32m$; $\theta ={30}^o$

Answer 1

The correct option is A $17.32m$; $\theta ={30}^o$

Since, Hypotenuse$=20m$
and Height=$10m$
$\therefore sin\theta$$=\frac{10}{20}$
$\Rightarrow sin\theta$$=\frac{1}{2}$
But we know that
$sin{30}^o=$$\frac{1}{2}$

Hence, we can say that
$\theta ={30}^o$
Therefore,
Base
$=20cos{30}^{o}m$
$=20\left(\frac{\sqrt{3}}{2}\right)$
$=10\left(1.732\right)$
$=17.32m$