# If sides A and B of a triangle have lengths of 18 and 12 respectively, and the angle between them is (2pi)/3, then what is the area of the triangle?

##### 1 Answer
Jul 8, 2018

Area of triangle color(chocolate)(A_t = 93.53 sq. units

#### Explanation:

Formula for area of triangle ${A}_{t} = \left(\frac{1}{2}\right) a b \sin C$

Given $a = 18 , b = 12 , \hat{C} = \frac{2 \pi}{3}$

${A}_{t} = \left(\frac{1}{2}\right) \cdot 18 \cdot 12 \cdot \sin \left(\frac{2 \pi}{3}\right)$

${A}_{t} = \frac{9 \cdot 12 \cdot \sqrt{3}}{2} = 54 \sqrt{3} = 93.53$