detect airplanes up to 50 miles away. your in a airplane flying straight line from city 60 miles north of the tower to a second city 70 miles east of the tower.

Question

An air traffic control tower can detect airplanes up to 50 miles away. your in a airplane flying straight line from city 60 miles north of the tower to a second city 70 miles east of the tower. During how much of the flight will you be detected by this tower?

Answer 1

With respect to the tower, the line of travel of the airplane is 

y=-(6/7)x + 60

The range of the tower's visibility is

x²+y²=50²

You now have a system of equations that can be solved for x

 

you should find that the plane is visible from approximately x=14mile to x=46 miles

This corresponds to a travel distance of approximately 52 miles of your 92 mile journey, or 57% of your flight time.