# A triangle has sides A, B, and C. Sides A and B have lengths of 5 and 7, respectively. The angle between A and C is (17pi)/24 and the angle between B and C is  (pi)24. What is the area of the triangle?

Mar 26, 2018

color(green)("Area of the given triangle " A_t = 12.37 " sq units"

#### Explanation:

$\hat{A} = \frac{\pi}{24} , a = 5 , \hat{B} = \frac{17 \pi}{24} , b 7$

$\hat{C} = \pi - \frac{\pi}{24} - \frac{17 \pi}{24} = \frac{\pi}{4}$

We will use the formila two sides and the included angle to find the area of the given triangle.

${A}_{t} = \left(\frac{1}{2}\right) \cdot a \cdot b \cdot \sin C = \left(\frac{1}{2}\right) \cdot 5 \cdot 7 \cdot \sin \left(\frac{\pi}{4}\right) = 12.37 \text{ sq units}$