Question

The measure of $\angle B$ in the given triangle (in degrees) is ___.

• A. ${50}^{\circ }$
• B. ${60}^{\circ }$
• C. ${90}^{\circ }$
• D. ${40}^{\circ }$

Answer 1

The correct option is B ${60}^{\circ }$

In the given triangle,
$A{B}^2=8^2=64,A{C}^2={15}^2=225,andB{C}^2={17}^2=289.$

We know that if in a triangle, square of one side is equal to the sum of the squares of the other two sides, then the angle opposite the first side is a right angle.

Since $B{C}^2=A{C}^2+A{B}^2,$ $△ABC$ is a triangle which is right-angled at A.

$\Rightarrow \angle A={90}^{\circ }$

Now, using angle sum property in $△ABC,$ we have

$\angle ABC+\angle ACB+\angle BAC={180}^{\circ }$

$\Rightarrow \angle B+{30}^{\circ }+{90}^{\circ }={180}^{\circ }$

$\Rightarrow \angle B={180}^{\circ }-{120}^{\circ }={60}^{\circ }$