In triangle abc, ab=5 bc=9 and ac=8

Choose the angle measures from greatest to least

2 answers

The more standard way to state your question would have been..
In triangle ABC , a=9, b=8, and c=5
that is, let A, B, and C be the vertices, and a, b, and c be the sides opposite those vertices.

I usually find the largest angle first, using the cosine law. In this case angle A
9^2 = 5^2 + 8^2 - 2(5)(8)cos A
cos A = (25 + 64 - 81)/(80 = 8/80 = 1/10
angle A = 84.26°

Now use the Sine Law to find a second angle, the third is then easy.
AC=5 BC=9 AC=8