Word Problem

Question

Two planes take off at a ny airport. The first plane climbs at an angle of 45 degrees with respect to the ground and reaches an altitude of 5600 feet. The second plane climbs at an angle of 60 degress with respect to the ground and reaches an altitude of 8200 feet. To the nearest foot, which plane covers a longer gorund distance?

Answer 1

It might appear at first we need to know the velocity of the planes, but this can be reduced to a simple trigonometry problem.

 

If was examine plane 1's flight path, then we see it forms a right triangle with a height of 5600 and and opposite angle of 45 degrees and the adjacent side as the ground distance.  Then we can see that the Tangent function, which is opposite/adjacent will let us form an equation to solve the ground distance.

 

Tan(angle)= Altitude / x   --->   x= Altitude / Tan(angle)

 

So plane 1 covers x = 5600 / Tan(45) = 5600, and plane 2 covers x = 8200 / Tan(60) = 4734.

 

Thus plane 1 covers 866 more feet than plane 2.