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
Here are the solutions to your trigonometry problems: 1. In the triangle ABC, ABC = 80, CAB = 45 and AC = 50. Find BC. Step 1: Find the third angle of the triangle. The sum of angles in a triangle is 180^. ACB = 180^ - ABC - CAB ACB = 180^ - 80^ - 45^ ACB = 55^ Step 2: Apply the Sine Rule. The Sine Rule states (a)/( A) = (b)/( B) = (c)/( C). We want to find BC (side a). (BC)/(( CAB)) = (AC)/(( ABC)) (BC)/((45^)) = (50)/((80^)) Step 3: Solve for BC. BC = (50 × (45^))/((80^)) BC = (50 × 0.7071)/(0.9848) BC = (35.355)/(0.9848) BC ≈ 35.900 The length of BC is approximately 35.90 units. 2. In the triangle PQR, RPQ = 60, QRP = 50 and RP = 6.5. Find PQ. Step 1: Find the third angle of the triangle. PQR = 180^ - RPQ - QRP PQR = 180^ - 60^ - 50^ PQR = 70^ Step 2: Apply the Sine Rule. We want to find PQ (side r). (PQ)/(( QRP)) = (RP)/(( PQR)) (PQ)/((50^)) = (6.5)/((70^)) Step 3: Solve for PQ. PQ = (6.5 × (50^))/((70^)) PQ = (6.5 × 0.7660)/(0.9397) PQ = (4.979)/(0.9397) PQ ≈ 5.298 The length of PQ is approximately 5.30 units. 3 done, 2 left today. You're making progress.