Question

In a $△ABC,\angle A={60}^{\circ },\angle B={30}^{\circ }and\angle C={90}^{\circ }.$ Find the length of BC when AB = 16 m .

• A. $3\sqrt{3}m$
• B. $8\sqrt{3}m$
• C. $6\sqrt{3}m$
• D. $7\sqrt{3}m$

Answer 1

The correct option is B $8\sqrt{3}m$

We have theorem :

"If the angles of a triangle are 30, 60 and 90 degrees, then the side opposite to 60 degree is $\frac{\sqrt{3}}{2}$ times the hypotenuse"

Here, hypotenuse = AB= 16 m

So, BC= $\frac{\sqrt{3}}{2}\times 16=8\sqrt{3}m$