Answer: The angle between PC and the face PSDA is 90 degrees.
Step-by-step explanation:
To find the angle between PC and the face PSDA, you can use the law of cosines since we have a triangle with sides PC, PD, and CD.
1. First, determine the length of PD using the Pythagorean theorem:
PD^2 = PC^2 + CD^2
PD^2 = 8^2 + 16^2
PD^2 = 64 + 256
PD^2 = 320
PD = √320
PD = 8√5 cm
2. Next, calculate the cosine of the angle ∠PCD using the law of cosines:
cos(∠PCD) = (PC^2 + CD^2 - PD^2) / (2 * PC * CD)
cos(∠PCD) = (8^2 + 16^2 - 320) / (2 * 8 * 16)
cos(∠PCD) = (64 + 256 - 320) / 256
cos(∠PCD) = 0
3. Since the cosine of the angle is 0, the angle ∠PCD is 90 degrees.
