Question

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

Answer 1

Given the 3 sides, we must find the 3 angles A, B and C.
Use the trig Identity: a^2 = b^2 + c^2 - 2bc*cos A
16 = 25 + 36 - 2.(5).(6) . cos A = 61 - 60. cos A
cos A = 45/60 = 0.75 --> A = 41.40 deg
To find angle B, use the trig Identity a/sin A = b/sin B.
4/sin 41.40 = 4/0.66 = 5/sin B --
sin B = (5).(0.66)/4 = 0.825 --> B = 55.59 deg.
C = 180 - B - C = 180 - 41.40 - 55.59 = 83.01 deg
Check
a/sin A = c /sin C --> 4/0.66 = 6/sin C -->
sin C = (0.66) . (6)/4 = 0.99 --> C # 82.00 deg