Final answer:
To find the length of side QR in triangle PQR, one can use the area to calculate the height and then apply the Pythagorean theorem. Angle PQR can be found using the sine function and the calculated height.
Step-by-step explanation:
To solve for the length of side QR in triangle PQR given that side PQ is 9 cm, PR is 10 cm, and the area is 30 cm2, we can use Heron's formula or trigonometric relationships. However, since we have the area and only two sides, we can use the formula for the area of a triangle, which is Area = 1/2 × base × height. Without loss of generality, let's assume QR is the base. We then have to find the height corresponding to this base, which can be done by rearranging the area formula to get height = (2 × Area) / base. Once the height is found, we can use the Pythagorean theorem to find the length of QR.
To find ∠PQR (angle PQR), we can use the trigonometric function sine, as sin(∠PQR) = opposite side (height) / hypotenuse (PR). With the height calculated previously and the given length of PR, the angle can be determined using an inverse sine function.