Question

In right angle triangle $\Delta PQR$, right angle is at Q, and PQ=6cm, $\angle RPQ={60}^{\circ }$. Determine the length of QR and PR.

Answer 1

Let $PQR$ is a right angle triangle
$PQ=6cm,\angle RPQ={60}^{\circ }=\angle P$
$tan{60}^{\circ }=\frac{QR}{PQ}\Rightarrow \sqrt{3}=\frac{QR}{6}\Rightarrow QR=6\sqrt{3}$
$\sin {60}^{\circ }=\frac{QR}{PR}\Rightarrow \frac{\sqrt{3}}{2}=\frac{6\sqrt{3}}{PR}$
$\Rightarrow PR=6\sqrt{3}\times \frac{2}{\sqrt{3}}=6\times 2=12$
$\therefore$ The length of $QR$ is $6\sqrt{3}$ cms
$\therefore$ The length of $PR$ is $12$ cms