Question

In a $30-60-90$ triangle, the length of the hypotenuse is 6. What is the length of the shortest side?

• A. $2$
• B. $3$
• C. $3\sqrt{2}$
• D. $3\sqrt{3}$
• E. $6\sqrt{2}$

Answer 1

Answer: (B)

$3$

In the triangle the hypotenuse $=6$

the shortest side is the opposite to the angle ${30}^{\circ }$

$\Rightarrow sin{30}^{\circ }=\frac{1}{2}$

$\Rightarrow \frac{shortestside}{Hypotenuse}=\frac{1}{2}$

$\Rightarrow \frac{shortestside}{6}=\frac{1}{2}$

$\Rightarrow shortestside=\frac{6}{2}$

$\Rightarrow shortestside=3$

Ans is $Opt:\left[B\right]$