Final answer:
To find the area of ΔPQR, use the formula for the area of a triangle and trigonometry to calculate the height. Then, plug in the values to find the area and round to the nearest square inch.
Step-by-step explanation:
To find the area of ΔPQR, we can use the formula for the area of a triangle: A = 1/2 * base * height.
In this case, the base is the length of QR, which is equal to r, and the height is the perpendicular distance from P to QR.
We can find this height using trigonometry.
First, we can find the length of PQ using the Law of Cosines: PQ^2 = QR^2 + PR^2 - 2 * QR * PR * cos(∡P).
Plugging in the given values, we have PQ^2 = 38^2 + 77^2 - 2 * 38 * 77 * cos(57°). Solve for PQ to find the length of PQ.
Once we have PQ, we can find the height by using the formula: height = PQ * sin(∡P).
Finally, we can calculate the area by plugging in the values of r and the height into the formula A = 1/2 * r * height. Round the result to the nearest square inch to get the final answer.