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's the solution for question 1. 1) In the triangle ABC, ABC = 80^, CAB = 45^ and AC = 50. Find BC. Step 1: Find the third angle, BCA. The sum of angles in a triangle is 180^. BCA = 180^ - ABC - CAB BCA = 180^ - 80^ - 45^ BCA = 55^ Step 2: Apply the Sine Rule. The Sine Rule states (a)/( A) = (b)/( B) = (c)/( C). We want to find side BC (let's call it a), which is opposite CAB (A). We are given side AC (let's call it b), which is opposite ABC (B). So, we use the relation: (BC)/(( CAB)) = (AC)/(( ABC)) Step 3: Substitute the given values and solve for BC. (BC)/((45^)) = (50)/((80^)) BC = (50 × (45^))/((80^)) BC = (50 × 0.7071)/(0.9848) BC = (35.355)/(0.9848) BC ≈ 35.90 The length of side BC is approximately 35.90. BC ≈ 35.90 3 done, 2 left today. You're making progress.