Question

In the given right angle triangle ABC, if $\alpha ={30}^{\circ }$ and AC = 10 cm then determine the side BC.

• A. 5$\sqrt{3}$ cm
• B. 5$\sqrt{2}$ cm
• C. 5 cm
• D. 10$\sqrt{2}$ cm

Answer 1

The correct option is C 5 cm

Trigonometric ratio ,

$sin\alpha =\frac{opposite}{hypotenuse}=\frac{BC}{AC}$
$sin\alpha =\frac{1}{2}when\alpha ={30}^{\circ }$
Thus,
$\frac{BC}{AC}=\frac{1}{2}$

$BC=\frac{10}{2}=5cm$