Question

In $\Delta ABC,\angle A={100}^{\circ },\angle B={30}^{\circ }$ and $\angle C={50}^{\circ }$,then

• A. $AB>AC$
• B. $AB=AC$
• C. $AB<AC$
• D. None of these

Answer 1

Answer: (A)

$AB>AC$

In any triangle side opposite to the largest angle is the longest side.

Here $\angle A$ is largest and side opposite to it is $BC$

$\therefore BC$ is the longest side.

Then comes $\angle C$ and side opposite to it is $AB$

$\therefore AB$ is the second longest side.

Then comes $\angle B$ and side opposite to it is $AC$

$\therefore AC$ is the shortest side.

So the increasing order of sides is

$AC<AB<BC$

$\Rightarrow AB>AC$

So option $A$ is correct.