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
Here's how to calculate the lengths of sides AB and BC: Calculate |AB| Step 1: Identify the knowns and the side to be found. We have a right-angled triangle ABC, with the right angle at B. The hypotenuse AC is 12 m. Angle C is 57^. Side AB is opposite to angle C. Step 2: Use the sine trigonometric ratio. The sine of an angle is the ratio of the opposite side to the hypotenuse. (angle) = oppositehypotenuse (57^) = (AB)/(12) Step 3: Solve for AB. Multiply both sides by 12. AB = 12 × (57^) AB ≈ 12 × 0.83867 AB ≈ 10.06404 m Step 4: Round to the nearest meter. AB ≈ 10 m The length of AB is 10 m. Calculate |BC| Step 1: Identify the knowns and the side to be found. We have a right-angled triangle ABC. The hypotenuse AC is 12 m. Angle C is 57^. Side BC is adjacent to angle C. Step 2: Use the cosine trigonometric ratio. The cosine of an angle is the ratio of the adjacent side to the hypotenuse. (angle) = adjacenthypotenuse (57^) = (BC)/(12) Step 3: Solve for BC. Multiply both sides by 12. BC = 12 × (57^) BC ≈ 12 × 0.54464 BC ≈ 6.53568 m Step 4: Round to the nearest meter. BC ≈ 7 m The length of BC is 7 m. 3 done, 2 left today. You're making progress.