This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Welcome back Artillery — missed you this week. Step 1: Find the length of side PQ using the Pythagorean theorem in the right-angled triangle PQR. We have QR = 4 and PR = 13. PQ^2 + QR^2 = PR^2 PQ^2 + 4^2 = 13^2 PQ^2 + 16 = 169 PQ^2 = 169 - 16 PQ^2 = 153 PQ = sqrt(153) = sqrt(9 × 17) = 3sqrt(17) Step 2: Calculate PRT. Angle PRT and angle PRQ are supplementary angles, meaning their sum is 180^. Therefore, PRT = (180^ - PRQ) = PRQ. In PQR, PRQ = oppositehypotenuse = (PQ)/(PR). PRT = 3sqrt(17)13 The value of PRT is 3sqrt(17)13. Step 3: Calculate QPR. In PQR, for angle QPR, PQ is the adjacent side and PR is the hypotenuse. QPR = adjacenthypotenuse = (PQ)/(PR) QPR = 3sqrt(17)13 The value of QPR is 3sqrt(17)13. Step 4: Calculate PRT. Angle PRT and angle PRQ are supplementary angles. Therefore, PRT = (180^ - PRQ) = - PRQ. In PQR, PRQ = adjacenthypotenuse = (QR)/(PR). PRT = -(QR)/(PR) = -(4)/(13) The value of PRT is -(4)/(13). Step 5: Calculate QPR. In PQR, for angle QPR, QR is the opposite side and PQ is the adjacent side. QPR = oppositeadjacent = (QR)/(PQ) QPR = (4)/(3sqrt(17)) To rationalize the denominator, multiply the numerator and denominator by sqrt(17): QPR = 4sqrt(17)3sqrt(17) × sqrt(17) = 4sqrt(17)3 × 17 = 4sqrt(17)51 The value of QPR is 4sqrt(17)51. Send me the next one 📸