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
Step 1: Find the third angle in triangle PQR. The sum of angles in a triangle is 180^. PQR = 180^ - RPQ - QRP PQR = 180^ - 60^ - 50^ PQR = 70^ Step 2: Apply the Sine Rule to find PQ. The Sine Rule states that for a triangle with sides p, q, r and opposite angles P, Q, R: (p)/( P) = (q)/( Q) = (r)/( R) In triangle PQR, we want to find side PQ (let's call it r), and we know angle QRP (R). We also know side RP (let's call it q) and angle PQR (Q). (PQ)/(( QRP)) = (RP)/(( PQR)) Substitute the given values: (PQ)/((50^)) = (6.5)/((70^)) Solve for PQ: PQ = (6.5 × (50^))/((70^)) PQ = (6.5 × 0.7660)/(0.9397) PQ = (4.979)/(0.9397) PQ ≈ 5.30 units The length of PQ is approximately 5.30. What's next?