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
The length of side AC is 20 cm. Supporting Details: 1. Identify the knowns and unknowns: We have a right-angled triangle ABC, with the right angle at B. Angle C = 30° The side opposite to angle C (AB) = 10 cm. We need to find the length of the hypotenuse (AC). 2. Choose the appropriate trigonometric ratio: The sine function relates the opposite side, the hypotenuse, and the angle: sin(angle) = Opposite / Hypotenuse 3. Set up the equation: sin(C) = AB / AC sin(30°) = 10 / AC 4. Solve for AC: We know that sin(30°) = 1/2. So, 1/2 = 10 / AC To solve for AC, cross-multiply: 1 AC = 2 10 AC = 20 cm