Final answer:
In triangle PQR, with PM as the bisector of angle P, we can use the Angle Bisector Theorem and Law of Cosines to find the angle.
Step-by-step explanation:
In triangle PQR, PM is the bisector of angle P. Given that PQ is 5.6 cm, QR is 4 cm, and PM is 3 cm, we can find the angle.
Since PM is the angle bisector, it divides angle P into two equal angles. Let's call the angle on one side of PM as x. So, the other angle on the other side of PM is also x.
Using the Angle Bisector Theorem, we can set up the following proportion: PM/PQ = QR/PR
Substituting the given values, we have 3/5.6 = 4/PR
Cross-multiplying, we get 3PR = 5.6 * 4
Simplifying, we have PR ≈ 9.45 cm
Now, we can use the Law of Cosines to find angle P:
cos(P) = (QR^2 + PR^2 - PQ^2) / (2 * QR * PR)
Substituting the given values, we have cos(P) = (4^2 + 9.45^2 - 5.6^2) / (2 * 4 * 9.45)
Simplifying, we get cos(P) ≈ 0.939
Now, we can find the angle P by taking the inverse cosine of 0.939. Using a calculator, we find that the angle P is approximately 20.77 degrees.