Question

$\angle Q$ and $\angle R$ of a triangle PQR are ${25}^o$ and ${65}^o$. Is $△PQR$ a right angled triangle?
Moreover PQ is 4 cm and PR is 3 cm. Find QR.

Answer 1

Given :

In $△PQR$

$\angle PQR=25°,PQ=4cm$

$\angle PRQ=65°,PR=3cm$

$\therefore \angle QPR=180°-90°=90°$

$\therefore △PQR$ is a right angle triangle.

So, By pythagoras theorem,

${QR}^2={PQ}^2+{PR}^2$

${QR}^2=4^2+3^2$

${QR}^2=25$

$QR=5cm$