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# $ABC$ is a $\Delta$le.Its area is 12sqcm and base is 6cm.The difference of base angle is $60^{\large\circ}$.If $A$ be the angle opposite to the base,then the value of $8\sin A-6\cos A$ is

$(a)\;2\qquad(b)\;4\qquad(c)\;3\qquad(d)\;1$

Given :
$a=6$cm
Area $\Delta=12cm^2$
$B-C=60^{\large\circ}$
Now $\Delta=\large\frac{1}{2}$$ab\sin C \qquad\;\;\;=\large\frac{1}{2}$$a.k\sin B\sin C$
$\qquad\;\;\;=\large\frac{1}{2}$$a.\large\frac{a}{\sin A}$$\sin B\sin C$