Question

In the given right angled triangle ABC, if $\alpha ={30}^{\circ }$ and $AC=10cm$ then the side $BC$ would be ___ $cm$

Answer 1

Trigonometric ratio,
$\sin \alpha =\frac{\text{opposite side}}{\text{hypotenuse}}=\frac{BC}{AC}$
$\because \sin \alpha =\frac{1}{2}$ when $\alpha ={30}^{\circ }$
Thus, $\frac{BC}{AC}=\frac{1}{2}$
$\Rightarrow BC=\frac{AC}{2}=\frac{10}{2}=5cm$