An air traffic controller is tracking two planes. to start, playing a is at an altitude of 2814 ft and plan b is just taking off. plan a is gaining altitude at 30.5 feet per second in playing day is gaining altitude at 80.75 feet per second. how many seconds will pass before the planes are on the same altitude

Model the altitude of each plane with a linear equation.
The initial altitude is the 'y-intercept'.
The rate of elevation is the slope.

Plane A:  y = 30.5x + 2814

Plane B:  y = 80.75x

The planes will be at same altitude when the y values are equal.
80.75x = 30.5x + 2814

Solve equation for 'x'.
80.75x - 30.5x = 2814
50.25x = 2814
x = (2814/50.25) = 56

It will take 56 seconds before planes are at same altitude.

40 & 50 in the right corner are the complementary angles as when placed in a sum (added together) they make 90°