Question

An airplane is 275 miles from the airport to get to it present position the plane flew 125 miles due south from the airport and then flew due west. To the nearest mile how far west did the plane fly?

A-50 miles
B-77 miles
C-245 miles
D-302 miles

Answer 1

(C) 245 miles

Explanation:

We can view the starting and ending flight points as the hypotenuse of a right-angle triangle. Since the plane flew 125 miles south, the height of the triangle is 125 and we are given the hypotenuse as 275

If we designate the height as a and the hypotenuse as h, and the base as b then
h² = a² + b² by the Pythagorean theorem

or

b² = h² - a² ==> (h + a)(h - a) {x² - y² = (x + y) (x -y)}

Substituting known values
b² = 275² - 125² = (275 + 125)(275-125) = 400 x 150 = 60,000

b = √60000 = 244.94 and the closest answer is C: 245 miles