Question

Which is an expression for the area of Triangle ABC?

Answer 1

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:

`\begin{gathered} (b)/(\sin (\angle B))=(a)/(\sin (\angle A)) \\ (15)/(\sin(65))=(a)/(\sin (48)) \\ (15)/(\sin(65))\cdot\sin (48)=a \\ 12.3=a \end{gathered}`

Now we know two consecutive sides and the angle formed between them, we can compute the area of the triangle, as follows:

`\begin{gathered} A=(1)/(2)\cdot a\cdot b\cdot\sin (\angle C) \\ A=(1)/(2)\cdot(15)/(\sin(65))\cdot\sin (48)\cdot15\cdot\sin (67) \end{gathered}`

which is equivalent to the option C