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=(PQ)/(PR) \\ (1)/(2)=(PQ)/(4) \\ PQ=4\cdot(1)/(2) \\ =2 \end{gathered}`

Determine the length of side RQ by using trigonometry.

`\begin{gathered} \cos 30=(RQ)/(4) \\ \frac{\sqrt[]{3}}{2}=(RQ)/(4) \\ RQ=2\sqrt[]{3} \end{gathered}`

Thus length of each leg of triangle is,

`PQ=2`

and

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