Question

In a $△$ABC, $\angle$ABC = ${30}^{\circ }$ and $\angle$ACB = ${45}^{\circ }$. Which is the longest side in this triangle?

• A. AB
• B. BC
• C. CA
• D. All are same in length

Answer 1

The correct option is B BC

Sum of all angles in a triangle is ${180}^{\circ }$.
$\angle$BAC + $\angle$CAB + $\angle$CBA = ${180}^{\circ }$
$\angle$BAC + ${30}^{\circ }$ +${45}^{\circ }$ = ${180}^{\circ }$
$\angle$BAC = ${180}^{\circ }-({30}^{\circ }+{45}^{\circ })={105}^{\circ }$.

The side opposite to the largest angle will be the longest.
Side opposite to $\angle$BAC = BC.
Hence, BC is the longest side.