Exercise 9 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 ∠ N, MP, and NP one at a time.

Finding m ∠ N

We can find the third interior angle using the Triangle Angle Sum Theorem. 180- 111- 27= 42^(∘)

Finding MP

Now that we know the measure of ∠ N, we can find MP using the Law of Sines. sin N/MP =sin P/MN Let's substitute MN= 50, m ∠ P = 111, and m ∠ N = 42 to isolate MP.

Finding NP

Finally, we can repeat using the Law of Sines to find NP. sin P/MN =sin M/NP Let's substitute MN= 50, m ∠ P = 111, and m ∠ M = 27 to isolate NP.

Completing the Triangle

With all these calculated, we can complete our diagram.