10th Class Mathematics Triangles Question Bank MCQs - Triangles

In \[\Delta ABC,\] \[AB=6\sqrt{3}cm,\] \[AC=12cm\]and \[\text{BC}=\text{6 cm}\]. The angle B is: (NCERT EXERCISE; CBSE 2020)

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

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

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

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

Correct Answer: C

Solution :

[c] Here, \[{{(AB)}^{2}}={{(6\sqrt{3})}^{2}}=108,\,\,A{{C}^{2}}={{(12)}^{2}}=144\]

and \[{{(BC)}^{2}}={{(6)}^{2}}=36\]

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

\[\therefore \,\,\,\,\,\Delta ABC\] is a right triangle with \[\angle B=90{}^\circ \].