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 ABC with right angle at C. Given: BC = 10 m (one leg), AB = 100sqrt(10) m (hypotenuse). Find CA (other leg). Step 2: Apply Pythagorean theorem. AC^2 + BC^2 = AB^2 Step 3: Substitute given values (include units). AC^2 + (10\ m)^2 = (100sqrt(10)\ m)^2 Step 4: Calculate each term. AC^2 + 100\ m^2 = 10000 × 10\ m^2 AC^2 + 100\ m^2 = 100000\ m^2 Step 5: Solve for AC^2. AC^2 = 100000\ m^2 - 100\ m^2 AC^2 = 99900\ m^2 Step 6: Take square root (include units). AC = sqrt(99900)\ m Step 7: Simplify sqrt(99900). 99900 = 100 × 999 = 2^2 × 5^2 × 3^3 × 37 = 2^2 × 5^2 × 3^2 × (3 × 37) sqrt(99900) = sqrt(2^2) × 5^2 × 3^2 × 111 = 2 × 5 × 3 × sqrt(111) = 30sqrt(111) Step 8: Final answer (with units). AC = 30sqrt(111)\ m 30sqrt(111) m