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
Step 1: Identify the right triangle and the Pythagoras theorem. Triangle ABC is right-angled at C, with hypotenuse AB. AB^2 = AC^2 + BC^2 Step 2: Substitute the given lengths. AB = 10 cm, AC = 8 cm. (10\ cm)^2 = (8\ cm)^2 + BC^2 Step 3: Calculate the squares. 100\ cm^2 = 64\ cm^2 + BC^2 Step 4: Isolate BC^2. BC^2 = 100\ cm^2 - 64\ cm^2 BC^2 = 36\ cm^2 Step 5: Take the square root (positive length). BC = sqrt(36\ cm)^2 BC = 6\ cm 6\ cm