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Leviafan [203]
3 years ago
10

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. Angle ABC

=150°. Calculate the area of triangle ABC.
a)
40 km2
b)
30 km2
c)
10 km2

Mathematics
1 answer:
In-s [12.5K]3 years ago
6 0

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.

A=\frac{1}{2}a\cdot c\cdot\text{sin}(b), where angle b is angle between sides a and c.

For our given triangle a=5,c=8 and measure of angle b is 150 degrees.

A=\frac{1}{2}(5)\cdot (8)\cdot\text{sin}(150^{\circ})

A=5\cdot 4\cdot(0.5)

A=10

Therefore, the area of the triangle ABC is 10 square kilo-meters and option 'c' is the correct choice.

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