Find the area of the triangle. If necessary, round the answer to two decimal places.
-$$\alpha = 23 ^ { \circ } , b = 9 , c = 2$$
A) $3.52$
B) $3.50$
C) $3.51$
D) $3.53$

Question

Quizplus · Accepted Answer

Using the Law of Sines, we can find the height $h$ of the triangle relative to base $c$. First, we find angle $\beta$ using the fact that the sum of angles in a triangle is $180^\circ$. So, $\beta = 180^\circ - 90^\circ - 23^\circ = 67^\circ$. Then, $h = b \sin(\alpha) = 9 \sin(23^\circ)$. The area of the triangle is $\frac{1}{2}bc\sin(\alpha) = \frac{1}{2} \times 9 \times 2 \times \sin(23^\circ) \approx 3.52$.

Find the Area of the Triangle α=23∘,b=9,c=2\alpha = 23 ^ { \circ } , b = 9 , c = 2α=23∘,b=9,c=2

Find the Area of the Triangle $\alpha = 23 ^ { \circ } , b = 9 , c = 2$