Expert: Scott A Wilson - 10/18/2009

Question
In triangle ABC, a = 5, b = 9, and c = 6. Find angle A, angle B, and angle C.
Express the trig ratio in terms of the same trig ratio of a reference angle: tan 336

Answer
I used one of the law of cosines:
Given a triangle with sides a, b, c and opposite angles A, B, C,
a² + b² - 2abcos(C) = c².

I applied to to each of the angles, giving
cos(A) = (b² + c² - a²)/(2bc),
cos(B) = (c² + a² - b²)/(2ca), and
cos(C) = (a² + b² - c²)/(2ab).

For example, this means cos(A) = (9² + 6² - 5²)/(2*9*6) = 0.85185.
A = arccos(0.95195) = 0.55 radians.

The result is A is 0.55 radians, B is 1.91 radians, and C is 0.68 radians.
That is, respectively, 31.6°, 109.5°, and 38.9°.  They total to 180°

I'm not sure what it means when is says to express the trig ratio to a reference angle
or what tan 336 has to do with it.  I can say tan 336 = -0.151558634.