question_answer

In \[\Delta ABC,\]  \[AB=6\sqrt{3}cm,\] \[AC=12cm,\] and \[\text{BC}=\text{6 cm}\]. The angle B is:

A) \[120{}^\circ \]

B) \[60{}^\circ \]

C) \[90{}^\circ \]

D) \[45{}^\circ \]

Correct Answer: C

Solution :

[c] \[A{{C}^{2}}=144\,c{{m}^{2}},\]

\[A{{B}^{2}}=108\,c{{m}^{2}}\]

\[B{{C}^{2}}=36\,c{{m}^{2}}\]

Now  \[A{{B}^{2}}+B{{C}^{2}}=144=A{{C}^{2}}\]

\[\therefore \,\,\,\,\,\,\,\,\,\,\,\angle B=90{}^\circ \]