In ∆ABC, ∠A = 40° and ∠B = 60°.

Question:

In ABC, ∠A = 40° and ∠B = 60°. Then the longest side of ∆ABC is

(a) BC
(b) AC
(c) AB
(d) cannot be determined

Solution:

(c) AB

In triangle $\mathrm{ABC}$, we have:

$\angle A=40^{\circ}, \angle B=60^{\circ} \quad \ldots$ (Given)

Here, $\angle A+\angle B+\angle C=180^{\circ}$

$\Rightarrow 60^{\circ}+40^{\circ}+\angle C=180^{\circ}$

 

$\Rightarrow \angle C=80^{\circ}$

$\therefore$ The side opposite to $\angle C$, i.e., $\mathrm{AB}$, is the longest side of triangle $\mathrm{ABC}$.

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