Question

If in ∆PQR, ∠P = 70° and ∠R = 30°, then the longest side of ∆PQR is ___________.

Answer 1

In ∆PQR,

$\angle \mathrm{P}+\angle \mathrm{Q}+\angle \mathrm{R}=180°$ (Angle sum property of a triangle)

$\therefore 70°+\angle \mathrm{Q}+30°=180°$

$\Rightarrow \angle \mathrm{Q}+100°=180°$

$\Rightarrow \angle \mathrm{Q}=180°-100°=80°$



So, ∠Q is the greatest angle in the ∆PQR.

We know that, in a triangle the greater angle has the longer side opposite to it.

∴ PR is the longest side of ∆PQR.

If in ∆PQR, ∠P = 70° and ∠R = 30°, then the longest side of ∆PQR is ___PR___.