Question

Find the length of each leg.What is the length of PQ? do not include units (units) in your answer.

Answer 1

For angle 30 degree side PQ is perpendicular side, PR is hypotenuse side and RQ is base side.

Determine the length of side PQ by using trigonometry.

$\begin{gathered} \sin 30=\frac{PQ}{PR} \\ \frac{1}{2}=\frac{PQ}{4} \\ PQ=4\cdot\frac{1}{2} \\ =2 \end{gathered}$

Determine the length of side RQ by using trigonometry.

$\begin{gathered} \cos 30=\frac{RQ}{4} \\ \frac{\sqrt[]{3}}{2}=\frac{RQ}{4} \\ RQ=2\sqrt[]{3} \end{gathered}$

Thus length of each leg of triangle is,

$PQ=2$

and

$RQ=2\sqrt[]{3}$