In the triangle △ABC, introduce the notations a=|BC|, b=|CA|, c=|AB|, as well as ∠A=α , ∠B=β and ∠C=γ. Find c , given that angle ∠C is acute and a=6, b=7 and sin γ=1/9.

Answer 1

Use the Pythagorean Theorem to compute cos angle C.

Then use the Law of Cosines to compute c.