# How do you solve the triangle given a = 4, b = 5, and c = 6?

Jun 21, 2018

#### Answer:

color(indigo)(hat A = 41.41^@, hat B = 55.77^@, hat C = 82.82^@

#### Explanation:

$a = 4 , b = 5 , c = 6$

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

$\hat{C} = {\cos}^{-} 1 \left(\frac{{4}^{2} + {5}^{2} - {6}^{2}}{2 \cdot 4 \cdot 5}\right) = {82.82}^{\circ}$

$\hat{B} = {\cos}^{-} 1 \left(\frac{{4}^{2} + {6}^{2} - {5}^{2}}{2 \cdot 4 \cdot 6}\right) = {55.77}^{\circ}$

$\hat{A} = 180 - 82.82 - 55.77 = {41.41}^{\circ}$