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 for each problem using the Sine Rule and other appropriate rules, with answers rounded to the nearest whole number. The Sine Rule states: (a)/( A) = (b)/( B) = (c)/( C) The sum of angles in a triangle is 180^: A + B + C = 180^ The Cosine Rule states: c^2 = a^2 + b^2 - 2ab C --- 1) Given: a = 24.5 cm, B = 44^, C = 76^ Step 1: Find angle A. Using the sum of angles in a triangle: A = 180^ - B - C A = 180^ - 44^ - 76^ A = 180^ - 120^ A = 60^ Step 2: Find side b using the Sine Rule. (b)/( B) = (a)/( A) b = (a B)/( A) b = 24.5 cm × 44^ 60^ b = (24.5 × 0.694658)/(0.866025) b ≈ 19.65 cm