Question

In $△$ABC, if $\angle$A = ${45}^{\circ }$ and $\angle$B = ${70}^{\circ }$, then the shortest and the longest sides of the triangle, respectively, are:

• A. AB, BC
• B. BC, AC
• C. AB, AC
• D. None of these

Answer 1

The correct option is B

BC, AC

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 = ${70}^{\circ }$
Therefore, $\angle$C = ${180}^{\circ }$ - ${45}^{\circ }$ - ${70}^{\circ }$
= ${65}^{\circ }$

Hence, the side opposite to $\angle$A, i.e. BC, is the smallest and the side opposite to $\angle$B, i.e. AC, is the largest .