Please consider the attached graph.
We have been given that a helicopter flies 8 km due north from A to B. It then flies 5 km from B to C and returns to A as shown in the figure. The measure of angle ABC is 150°. We are asked to find the area of triangle ABC.
We will use trigonometric area formula to solve our given problem.
[tex]A=\frac{1}{2}a\cdot c\cdot\text{sin}(b)[/tex], where angle b is angle between sides a and c.
For our given triangle [tex]a=5,c=8[/tex] and measure of angle b is 150 degrees.
[tex]A=\frac{1}{2}(5)\cdot (8)\cdot\text{sin}(150^{\circ})[/tex]
[tex]A=5\cdot 4\cdot(0.5)[/tex]
[tex]A=10[/tex]
Therefore, the area of the triangle ABC is 10 square kilo-meters and option 'c' is the correct choice.
