The addition of the 3 angles of a triangle is 180°
∠A + ∠B + ∠C = 180°
∠B = 180° - 48° - 67°
∠B = 65°
From the law of sines:
[tex]\begin{gathered} \frac{b}{\sin (\angle B)}=\frac{a}{\sin (\angle A)} \\ \frac{15}{\sin(65)}=\frac{a}{\sin (48)} \\ \frac{15}{\sin(65)}\cdot\sin (48)=a \\ 12.3=a \end{gathered}[/tex]
Now we know two consecutive sides and the angle formed between them, we can compute the area of the triangle, as follows:
[tex]\begin{gathered} A=\frac{1}{2}\cdot a\cdot b\cdot\sin (\angle C) \\ A=\frac{1}{2}\cdot\frac{15}{\sin(65)}\cdot\sin (48)\cdot15\cdot\sin (67) \end{gathered}[/tex]
which is equivalent to the option C
