Answer
$9.1 \text{in.}^2 $
Work Step by Step
When the two sides let's say a and b and the angle C are given, then the area $\bf{A}$ can be calculated as:
$A=\dfrac{1}{2} ab \sin \text{C}$
From the given figure, we have: $ a= 10 \ \text{in.}; b = 7 \ \text{in.} ; C= 15^{\circ}$
$A=\dfrac{1}{2} (10) (7) \sin 15^{\circ} \approx 9.1 \text{in.}^2 $
