A triangle has sides A, B, and C. Sides A and B have lengths of 4 and 5, respectively. The angle between A and C is (5pi)/24 and the angle between B and C is  (3pi)/8. What is the area of the triangle?

Jul 17, 2017

The area is $= 9.66 {u}^{2}$

Explanation:

The dimensions of the triangle are

Side $a = 4$

Side $b = 5$

Angle $\hat{B} = \frac{5}{24} \pi$

Angle $\hat{A} = \frac{3}{8} \pi$

Therefore,

Angle $\hat{C} = \pi - \left(\frac{5}{24} \pi + \frac{3}{8} \pi\right)$

$= \pi - \frac{7}{12} \pi$

$= \frac{5}{12} \pi$

The area of the triangle is

$= \frac{1}{2} \cdot a \cdot b \cdot \sin \hat{C}$

$= \frac{1}{2} \cdot 4 \cdot 5 \cdot \sin \left(\frac{5}{12} \pi\right)$

$= 9.66 {u}^{2}$