When flying at an altitude of 5 miles, the lines of sight to the horizon looking north and south make about a 173.7 degree angle. how much of the longitude line directly under the plane is visible from 5 miles high?

5 miles high is one of the sides of a triangle depending on accuracy level

h^2=x^2+y^2

we don't have 2 distances

Tan A=O/a

O=a tan A

We solve for O because the angle is at the top of the line going up and we want the opposite angle that is along the ground

O=5*tan (173.7/2) = 90.854033512

The distance he can see is:

90.85*2~181.7 miles

Now we need to find the distance between lines:

The north south distance between each line is 69 miles

thus the number of degrees he will see will be:

181.7/69

=2 19/30