Find the area of the triangle. If necessary, round the answer to two decimal places.
-$$\alpha = 83 ^ { \circ } , b = 9 , \mathrm { c } = 6$$
A) $26.80$
B) $27.01$
C) $3.29$
D) $53.60$

Question

Quizplus · Accepted Answer

Using the Law of Sines, we can find the height $h$ of the triangle relative to base $c$: $h = b \sin(\alpha)$. Then, the area $A$ is $\frac{1}{2}ch$. With $\alpha = 83^\circ$, $b = 9$, and $c = 6$, we get $h = 9 \sin(83^\circ) \approx 8.95$, and $A \approx \frac{1}{2} \cdot 6 \cdot 8.95 \approx 26.85$, which rounds to $26.80$.

Find the Area of the Triangle α=83∘,b=9,c=6\alpha = 83 ^ { \circ } , b = 9 , \mathrm { c } = 6α=83∘,b=9,c=6

Find the Area of the Triangle $\alpha = 83 ^ { \circ } , b = 9 , \mathrm { c } = 6$