MCQ
Tick the correct answer and justify : $\text{In}\ \triangle\text{ABC},\ \text{AB}=6\sqrt{3}\ \text{ cm},AC = 12 \ cm$ and $BC = 6 \ cm.$ The angle $B$ is :
- A$120^\circ$
- B$60^\circ$
- ✓$90^\circ$
- D$45^\circ$
✓
Answer
Correct option: C.
$90^\circ$
Given that, $\text{AB}=6\sqrt{3}\text{ cm}, AC = 12 \ cm,$ and $BC = 6 \ cm$
We can observe that
$ A B^2=108$
$ A C^2=144$
And, $B C^2=36$
$A B^2+B C^2=A C^2$
The given triangle, $\triangle\text{ABC},$ is satisfying Pythagoras theorem.
Therefore, the triangle is a right triangle, right $-$ angled at $B$.
$\therefore\ \angle\text{B}=90^\circ$
Hence, the correct option is $(c).$
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