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

##### 1 Answer

Apr 25, 2015

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