Question

In $△\text{ABC}$ if $\text{AB=5 cm, BC=12 cm}$ and $\text{AC=13 cm}$, then $\angle \text{B}$ will be:

• A. ${120}^{\circ }$
• B. ${60}^{\circ }$
• C. ${90}^{\circ }$
• D. ${45}^{\circ }$

Answer 1

The correct option is C ${90}^{\circ }$

In $△ABC$,
${\left(AB\right)}^2+{\left(BC\right)}^2={\left(5\right)}^2+{\left(12\right)}^2$
$=25+144=169={13}^2=(AC{)}^2$
$⟹AC=13$

The converse of the Pythagoras theorem states that if the square of the longer side of a triangle is equivalent to the sum of its two shorter sides, then it must be a right triangle.
$\therefore △ABC$ is right angle triangle, in which $\angle B={90}^{\circ }$