Q:

An airplane takes off from an airport and travels 1100 miles east and then travels 600 miles north. This trip can be plotted on the coordinate plane, where the airport is the point (0, 0). The distance of the airplane to the airport can be found using the distance formula. Which other formula can be used?

Accepted Solution

A:
Answer:The distance of the airplane to the airport is 1421.26 miles.Step-by-step explanation:We are given the following information in the question:An airplane takes off from an airport and travels 1100 miles east and then travels 600 miles north. We could use the distance formula to calculate the distance between the airport and the airplane.Another method that can be used is the Pythagoras theorem.The attached image shows the scenario.According to Pythagoras theorem:In a right angled triangle the square of the hypotenuse is equal to  the sum of the squares of the other two sides.[tex]a^2 + b^2 = c^2[/tex], where c is the hypotenuse of the triangle that is the side opposite to the right angle.The distance between airport and airplane is the hypotenuse of the right angled triangle as show in the figure.[tex]\text{(Distance between airport and airplane)}^2 = (1100)^2 + (900)^2\\\\\text{Distance between airport and airplane)} = \sqrt{(1100)^2 + (900)^2} = 1421.26\text{ miles}[/tex]The distance of the airplane to the airport is 1421.26 miles.