A plane flies due east for 120 km from airport a to airport b it then flies due north for 280 km to airport c finally it flies directly back to airport a calculate the direct distance from airport to airport a give your answer to the nearest kilometre
If the distance from a to c is d, then
d^2 = 120^2 + 280^2
d = 40√58
To calculate the direct distance from airport A to airport A, we can use the concept of the Pythagorean Theorem.
Here's how we can approach the problem step by step:
1. Draw a diagram to visualize the scenario. Draw a horizontal line to represent the 120 km eastward journey from airport A to airport B. Then, draw a vertical line above airport B to represent the 280 km northward journey from airport B to airport C. Finally, connect the endpoint of the northward journey (airport C) back to airport A with a straight line.
2. With the diagram, we have created a right-angled triangle. The horizontal line represents the base of the triangle, the vertical line represents the height, and the line connecting airport C back to airport A represents the hypotenuse.
3. To find the direct distance from airport A to airport A, we need to find the length of the hypotenuse. We can use the Pythagorean Theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the other two sides of a right triangle.
4. In this case, we can calculate the hypotenuse as follows:
Hypotenuse^2 = Base^2 + Height^2
Hypotenuse^2 = 120^2 + 280^2
Hypotenuse^2 = 14400 + 78400
Hypotenuse^2 = 92800
5. Taking the square root of both sides of the equation, we find:
Hypotenuse = sqrt(92800)
Hypotenuse ≈ 304.8 km
Therefore, the direct distance from airport A to airport A is approximately 305 km (rounded to the nearest kilometer).