Determine the area of a triangle having the following measurements. Round your answer to two decimal places.
$C = 59 ^ { \circ } 24 ^ { \prime } , a = 6$, and $b = 14.5$
A) $37.44$ sq. units
B) $33.70$ sq. units
C) $29.95$ sq. units
D) $44.93$ sq. units
E) $41.19$ sq. units

Question

Quizplus · Accepted Answer

The area of a triangle can be calculated using the formula $ \frac{1}{2}ab \sin C $, where $a$ and $b$ are sides of the triangle, and $C$ is the angle between them. First, convert the angle to decimal form: $59^\circ 24' = 59.4^\circ$. Then, calculate the area: $ \frac{1}{2} \times 6 \times 14.5 \times \sin(59.4^\circ) \approx 37.44$ square units.

Determine the Area of a Triangle Having the Following Measurements C=59∘24′,a=6C = 59 ^ { \circ } 24 ^ { \prime } , a = 6C=59∘24′,a=6

Determine the Area of a Triangle Having the Following Measurements $C = 59 ^ { \circ } 24 ^ { \prime } , a = 6$