Exercise 8 Page 674

Let's begin by drawing △ ABC and labeling the length of the side and angles. We will also color code the opposite angles and sides. It will help us use the Law of Sines and Law of Cosines later.

Let's find the measures of ∠ B, AB, and BC one at a time.

Finding m ∠ B

We can find the third interior angle using the Triangle Angle Sum Theorem. 180- 32- 71= 77^(∘)

Finding AB

Now that we know the measure of ∠ B, we can find AB using the Law of Sines. sin C/AB =sin B/AC Let's substitute AC= 8, m ∠ B = 77, and m ∠ C = 71 to isolate AB.

Finding BC

Finally, we can repeat using the Law of Sines to find BC. sin A/BC =sin B/AC Let's substitute AC= 8, m ∠ B = 77, and m ∠ A = 32 to isolate BC.

Completing the Triangle

With all these calculated, we can complete our diagram.