A triangle has sides A, B, and C. Sides A and B have lengths of 3 and 5, respectively. The angle between A and C is (5pi)/8 and the angle between B and C is  (pi)/12. What is the area of the triangle?

1 Answer
Dec 20, 2016

$5.95$ square units

Explanation:

${A}_{\triangle} = \frac{1}{2} a b \sin C$

the angle to take as $C$ is the angle sandwiched between the $2$ given sides.

angle sandwiched between A and B = $\pi - \frac{5 \pi}{8} - \frac{\pi}{12}$

$= \frac{24 \pi}{24} - \frac{15 \pi}{24} - \frac{2 \pi}{24}$

$= \frac{7 \pi}{24}$

${A}_{\triangle} = \frac{3 \cdot 5}{2} \cdot \sin \left(\frac{7 \pi}{24}\right)$

$= 7.5 \sin \left(\frac{7 \pi}{24}\right)$

$= 5.95$ square units

(NB: when using $\pi$ as a measurement of angles, use the $R a d$ setting on your calculator)