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 = AC cos ${60}^{\circ }$ = $\frac{1}{2}$AC]

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

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