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

May 18, 2015

Use identity:

${c}^{2} = {a}^{2} + {b}^{2} - 2 a b . \cos C$
36 = 25 + 16 - 40.cos C --> cos C = 5/40 = 0.125 --> C = 82.82 deg

sin^20 C = 1 - cos^2 C = 0.98 -> sin C = 0.99

Next, use trig identity:$\sin \frac{A}{a} = \sin \frac{C}{c}$

$\sin A = 4 \left(\frac{0.99}{6}\right) =$0.66 -> A = 41.30

B = 180 - 41.30 - 82.82 = 55.88