# How do you find the area of the triangle given C=120^circ, a=4, b=6?

Mar 7, 2018

Area of triangle color(red)(A_t = 6 sqrt3 = 10.39 sq units

#### Explanation:

Area of a triangle can be calculated using formula

${A}_{t} = \left(\frac{1}{2}\right) a b \sin C$ having known SAS measurements.

$G i v e n : a = 4 , b = 6 , \hat{C} = {120}^{\circ}$

${A}_{t} = \left(\frac{1}{2}\right) 4 \cdot 6 \cdot \sin 120 = \left(\frac{1}{\cancel{2}}\right) \cdot {\cancel{24}}^{\textcolor{red}{12}} \cdot \sin \left(180 - 120\right)$

${A}_{t} = 12 \cdot \sin 60 = \left(\frac{{\cancel{12}}^{\textcolor{red}{6}} \cdot \sqrt{3}}{\cancel{2}}\right) = 6 \sqrt{3}$