Final answer:
The angles of ∡PQR are approximately 77.87°, 90°, and 11.13° from smallest to largest.
Step-by-step explanation:
The angles of ∡PQR can be found using the Law of Cosines. The Law of Cosines states that in a triangle, the square of one side is equal to the sum of the squares of the other two sides minus twice the product of the lengths of those two sides multiplied by the cosine of the angle between them.
In this case, we have PQ = 14, QR = 18, and PR = 24. Let's denote ∡PQR as angle P. Using the Law of Cosines, we can find the cosine of angle P:
cos P = (PR^2 + PQ^2 - QR^2) / (2 * PR * PQ)
Substituting the values we have: cos P = (24^2 + 14^2 - 18^2) / (2 * 24 * 14)
cos P = 0.225961
To find the angle P, we can use the inverse cosine function:
P = arccos(0.225961)
P ≈ 77.87°
Therefore, the angles of ∡PQR from smallest to largest are approximately 77.87°, 90°, and 11.13°.