Question

In $\Delta ABC,$ if $AB=6\sqrt{3}$ cm, $AC=12$ cm and $BC=6$ cm, then angle B is equal to:

• A. ${120}^0$
• B. ${90}^0$
• C. ${45}^0$
• D. ${60}^0$

Answer 1

The correct option is B ${90}^0$

$AC$ is the longest side
$AC=12\Rightarrow {\left(AC\right)}^2=144AB=6\sqrt{3},BC=6\Rightarrow {\left(AB\right)}^2+{\left(BC\right)}^2={\left(6\sqrt{3}\right)}^2+6^2=108+36=144\Rightarrow {\left(AC\right)}^2={\left(AB\right)}^2+{\left(BC\right)}^2$

We can see that pythagoras theorem is applicable in the given triangle.

So, by converse of pythagoras theorem, we have $\angle B={90}^{\circ }$ as $\angle B$ is opposite to the longest side $AC$.