Airplane is flying at an altitude of 3700 ft. The slanted distance directly to the airport is d ft. Express the distance h as function of d?

The Pythagorean theorem applies.
.. d^2 = 3700^2 +h^2
.. h = √(3700^2 -d^2)

let θ be the angle of elevation from airport to the plan, then:

sin(θ) = h/d

h = d * sin(θ)

Notice that h = altitude = 3700 ft is given, also the slanted distance is given as d thus:

d = 3700/sin(θ)

Now if you are asking the horizontal distance to the air port as h then consider a right triangle with hypotenuse = d , vertical leg = 3700 and the base = h, then:

d^2 = 3700^2 + h^2 => rearrange:

h^2 = d^2 - 3700^2

h = √(d^2 - 3700^2) ft

I hope this helps.

d² = h² + 3700²
h = √(d² - 3700²)