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: Visualize the movement and draw a diagram. The plane flies S 60^ E from point A to point B. This means it flies 60^ towards the East from the South direction. The total distance flown is 100 km. We can form a right-angled triangle where: • The hypotenuse is the distance from A to B (100 km). • One leg is the distance traveled South. • The other leg is the distance traveled East. The angle between the South line and the path AB is 60^. Step 2: Identify the required component. We need to find "how far east of A is B". This is the length of the side opposite the 60^ angle in our right-angled triangle. Step 3: Use trigonometry to find the distance East. Let d_E be the distance East. In a right-angled triangle, the sine of an angle is the ratio of the length of the opposite side to the length of the hypotenuse. () = oppositehypotenuse In this case, = 60^, the opposite side is d_E, and the hypotenuse is 100 km. (60^) = (d_E)/(100 km) Step 4: Calculate the distance East. d_E = 100 km × (60^) We know that (60^) = sqrt(3)2. d_E = 100 km × sqrt(3)2 d_E = 50sqrt(3) km Now, calculate the numerical value: d_E ≈ 50 × 1.7320508 km d_E ≈ 86.60254 km Step 5: Round the answer to the nearest kilometer. d_E ≈ 87 km The plane is approximately 87 km east of A. That's 2 down. 3 left today — send the next one.