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: Find the angle in radians. The formula for arc length s is s = r, where r is the radius and is the angle in radians. Given s = 10 cm and r = 4 cm. 10 = 4 = (10)/(4) = (5)/(2) radians = 2.5 radians Step 2: Convert the angle to degrees. To convert radians to degrees, multiply by (180^)/(). _degrees = (5)/(2) × (180^)/() _degrees = (450^)/() Using ≈ 3.14159: _degrees ≈ (450^)/(3.14159) _degrees ≈ 143.239^ Step 3: Find the area of the corresponding sector. The formula for the area of a sector A is A = (1)/(2)r^2, where is in radians. Given r = 4 cm and = (5)/(2) radians. A = (1)/(2)(4 cm)^2 ((5)/(2)) A = (1)/(2)(16 cm^2) ((5)/(2)) A = 8 cm^2 × (5)/(2) A = 4 cm^2 × 5 A = 20 cm^2 The angle subtended by the arc is 2.5 radians or (450)/() degrees. The area of the corresponding sector is 20 cm^2.