Final answer:
The angles of the triangle with vertices P(1, 0), Q(0, 3), and R(5, 5) can be found by first calculating the lengths of the sides of the triangle and then applying the Law of Cosines to determine each angle. Finally, the angles must be rounded to the nearest degree.
Step-by-step explanation:
To find the angles of the triangle with vertices P(1, 0), Q(0, 3), and R(5, 5), we can use the distances between the points to calculate the sides of the triangle and then apply the Law of Cosines to find the angles.
Step 1: Calculate the sides of the triangle
We calculate the sides of the triangle by finding the distance between each pair of points:
PQ = √[(0-1)2 + (3-0)2] = √(1 + 9) = √10
PR = √[(5-1)2 + (5-0)2] = √(16 + 25) = √41
QR = √[(5-0)2 + (5-3)2] = √(25 + 4) = √29
Step 2: Use the Law of Cosines to find each angle
For angle P, we use the sides PQ and PR, and opposite side QR:
cos(P) = (PQ2 + PR2 - QR2) / (2 * PQ * PR)
Substitute the known lengths:
cos(P) = (√102 + √412 - √292) / (2 * √10 * √41)
Solve for angle P and then similarly solve for angles Q and R using the respective sides and the Law of Cosines. Round each angle to the nearest degree.