Question

In △ABC, AB = $6\sqrt{3}$ cm, AC = 12 cm and BC = 6 cm. Then ∠B is
(a) 45^o
(b) 60^o
(c) 90^o
(d) 120^o

Answer 1

$$\begin{gathered} \mathrm{AB}=6\sqrt{3}\mathrm{cm} \\ \Rightarrow {\mathrm{AB}}^2=108{\mathrm{cm}}^2 \\ \mathrm{AC}=12\mathrm{cm} \\ \Rightarrow {\mathrm{AC}}^2=144{\mathrm{cm}}^2 \\ \mathrm{BC}=6\mathrm{cm} \\ \Rightarrow {\mathrm{BC}}^2=36\mathrm{cm} \\ \therefore {\mathrm{AC}}^2={\mathrm{AB}}^2+{\mathrm{BC}}^2 \end{gathered}$$
Since, the square of the longest side is equal to the sum of the square of two sides, so △ABC is a right angled triangle.
∴The angle opposite to AC i.e. ∠B = 90^o
Hence, the correct answer is option (c)