Question

In the adjoining figure, if BC = a, AC = b, AB = c and $\angle CAB={120}^{\circ }$, then the correct relation is-

• A. a² = b² + c² + 2 bc
• B. a² = b² + c² – 2 bc
• C. a² = b² + c² + bc
• D. a² = b² + c² – bc

Answer 1

The correct option is C

a² = b² + c² + bc

[C] Since ∠A is an obtuse angle in ΔABC, so

${BC}^2={AB}^2+{AC}^2+2AB.AD$

$={AB}^2+{AC}^2+2AB.\frac{1}{2}AC$

[ ∵$AD=ACcos{60}^{\circ }=\frac{1}{2}AC$]

$={AB}^2+{AC}^2+AB.AC$

$a^2=b^2+c^2+bc$.