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 solve part b) of the problem. Step 1: Determine the angle between the paths of Plane A and Plane B from the airport P. Plane A is on a bearing of 070^. Plane B is on a bearing of 162^. The angle APB is the difference between these bearings: APB = 162^ - 070^ = 92^ Step 2: Calculate the actual distance between Plane A and Plane B after 3 hours. From the previous part, we know: Distance PA (from P to A) = 1200 km Distance PB (from P to B) = 900 km We use the Law of Cosines in APB to find the distance AB: AB^2 = PA^2 + PB^2 - 2(PA)(PB)( APB) AB^2 = (1200)^2 + (900)^2 - 2(1200)(900)(92^) AB^2 = 1,440,000 + 810,000 - 2,160,000(92^) AB^2 = 2,250,000 - 2,160,000(-0.034899) AB^2 = 2,250,000 + 75,381.84 AB^2 = 2,325,381.84 AB = sqrt(2,325,381.84) AB ≈ 1524.92 km Step 3: Calculate the time it takes for Plane B to reach Plane A's position. Plane B travels at its original speed, which is 300 km/h. Time = DistanceSpeed Time = 1524.92 km300 km/h Time ≈ 5.083067 hours Step 4: Convert the time to hours and minutes, to the nearest minute. The time is 5 full hours. To find the minutes, multiply the decimal part by 60: 0.083067 hours × 60 minutes/hour ≈ 4.984 minutes Rounding to the nearest minute, this is 5 minutes. So, the time taken is 5 hours and 5 minutes. Step 5: Determine the length of AB on the scale drawing. The scale is 1 cm represents 200 km. Length on drawing = Actual distanceScale factor Length on drawing = 1524.92 km200 km/cm Length on drawing ≈ 7.62 cm The time it takes for Plane B to reach Plane A's position is 5 hours 5 minutes. The length of AB on the scale drawing is approximately 7.6 cm. Last free one today — make it count tomorrow, or type /upgrade for unlimited.