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
12. (a) Step 1: Identify the sides of the isosceles triangle. The ratio of the sides is 5:3:5. This means the two equal sides have a length proportional to 5, and the third side has a length proportional to 3. Let the sides be a=5x, b=5x, and c=3x. We need to find the angle between the two equal sides (i.e., the angle opposite side c). Step 2: Apply the Law of Cosines. The Law of Cosines states c^2 = a^2 + b^2 - 2ab . Substitute the side lengths: (3x)^2 = (5x)^2 + (5x)^2 - 2(5x)(5x) 9x^2 = 25x^2 + 25x^2 - 50x^2 9x^2 = 50x^2 - 50x^2 Step 3: Solve for . Divide both sides by x^2 (assuming x ≠ 0): 9 = 50 - 50 50 = 50 - 9 50 = 41