Question

In $\Delta ABC$, if ∠A = 45° and ∠B = 65°, then the shortest side of the triangle is _______.

Answer 1

As we know that the three angles of a triangle add up to ${180}^{\circ }$,
Also, the other two angles are given as,
$\angle$A = ${45}^{\circ }$ and $\angle$B = ${65}^{\circ }$
Therefore, $\angle$C = ${180}^{\circ }$ - ${45}^{\circ }$ - ${65}^{\circ }$ = ${70}^{\circ }$

Now,
$\angle C>\angle B>\angle A$
Hence, the side opposite to $\angle$A, i.e., BC is the smallest and the side opposite to $\angle$C, i.e., AB is the longest.