To find the length of SR in quadrilateral SRQP, we can use 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 two sides multiplied by the cosine of the enclosed angle.
In triangle SPQ, we can use the Law of Cosines to find the length of side SQ as follows: SQ^2 = SP^2 + PQ^2 - 2 * SP * PQ * cos(angle SPQ)
Using the given values: SP = 20cm PQ = 25cm angle SPQ = 82°
We can substitute these values into the equation and solve for SQ: SQ^2 = 20^2 + 25^2 - 2 * 20 * 25 * cos(82°) SQ^2 = 400 + 625 - 1000 * cos(82°) SQ^2 ≈ 196.785
Taking the square root of both sides, we find: SQ ≈ √196.785 SQ ≈ 14
Now, to find the length of SR, we can use the Law of Cosines in triangle PQR as follows: SR^2 = PQ^2 + QR^2 - 2 * PQ * QR * cos(angle PQR)
Using the given values: PQ = 25cm QR = 40cm angle PQR = 93°
Substituting these values into the equation and solving for SR: SR^2 = 25^2 + 40^2 - 2 * 25 * 40 * cos(93°) SR^2 = 625 + 1600 - 2000 * cos(93°) SR^2 ≈ 815.28
Taking the square root of both sides, we find: SR ≈ √815.28 SR ≈ 28.57
Therefore, the length of SR is approximately 28.57 cm. It seems like your teacher's answer of 31.4 cm might be a mistake, as the calculation using the Law of Cosines gives a different result.