Question

In a $△ABC$ in which $AC=5cm$ and $\angle BAC={60}^{\circ }$ and $BC-AB=1.2cm$. The, $AB$ is

• A. $3.18$
• B. $4.32$
• C. $5.12$
• D. None of these

Answer 1

The correct option is A $3.18$

Given : $AC=5cm$

$\angle BAC=60°$

$BC-AB=1.2cm$

$BC=1.2+AB$

$⟹\cos 60°=\frac{{AC}^2+{AB}^2-{BC}^2}{2AC\times AB}$

$⟹\frac{1}{2}=\frac{25+x^2-{(1.2+x)}^2}{2\times 5\times x}$

$⟹5x=25+x^2-1.44-x^2-2.4x$

$⟹7.4x=23.56$

$⟹x=3.18$

$\therefore AB=3.18,BC=4.38$