# How do you solve the triangle when given 3, 4, and 6?

Apr 2, 2018

color(blue)("Area of " Delta ~~) color(crimson)( 5.94 " sq units"

#### Explanation:

$a = 3 , b = 4 , c = 6$

Applying the law of cosines,

$\cos C = \frac{{c}^{2} - {a}^{2} - {b}^{2}}{2 \cdot a \cdot b}$

$\cos c = \frac{{6}^{2} - {3}^{2} - {4}^{2}}{2 \cdot 3 \cdot 4} = 0.1382$

$\hat{C} = {\cos}^{-} 1 \left(0.1382\right) = {1.4322}^{c}$

$\text{Area of } \Delta = \left(\frac{1}{2}\right) a b \sin C$

$\implies \left(\frac{1}{2}\right) \cdot 3 \cdot 4 \cdot \sin \left(1.4322\right) \approx 5.94 \text{ sq units}$