Question

what is the area of δabc? round to the nearest tenth of a square unit.
3.9 square units
8.4 square units
11.8 square units
17.7 square units
trigonometric area formula: area = \frac{1}{2}ab\sin(c)

Explanation:

Step1: Identify values for formula

Let $a = 2\sqrt{2}$, $b = 6$, and $C=80^{\circ}$.

Step2: Substitute into area formula

Area $=\frac{1}{2}\times(2\sqrt{2})\times6\times\sin(80^{\circ})$.
First, $\frac{1}{2}\times2\sqrt{2}\times6 = 6\sqrt{2}$.
Then, $\sin(80^{\circ})\approx0.9848$.
So area $=6\sqrt{2}\times0.9848$.
$6\sqrt{2}\approx6\times1.4142 = 8.4852$.
Area $\approx8.4852\times0.9848\approx8.4$ square - units.

Answer:

8.4 square units