Question

In a triangle $ABC,\angle ABC={50}^o,\angle BAC={30}^o$, then the shortest sides is

• A. $AB$
• B. $BC$
• C. $CA$
• D. $None$

Answer 1

The correct option is B $BC$

The side opposite to the largest angle is the longest side of the triangle and the side opposite to the smallest angle is the shortest side of the triangle.

By angle sum property,$\angle A+\angle B+\angle C={180}^{\circ }$

$\Rightarrow {30}^{\circ }+{50}^{\circ }+\angle C={180}^{\circ }$

$\Rightarrow \angle C={180}^{\circ }-{80}^{\circ }={100}^{\circ }$

The side opposite to the smallest angle $\left({30}^{\circ }\right)$ is the side $BC$