An airplane is coming in for a landing and the pilot knows she is 5473 m above the ground and she also knows that Angle of depression from the plane to the landing strip is 58º. How far is the plane from the landing strip?

so, essentially, the angle from the straight line the plane could be going at that moment down to the touch down point on the landing strip is 58 degrees.

that means the angle of elevation (between the line to the touch down point and the height "line" of the airplane) is 90-58 = 32 degrees

the height of the airplane (= distance from ground) is 5473 m.

now, we also know that the angle between height and the ground connection to the touch down point is 90 degrees (as height is always meshed straight up/down).

so, we know even the third angle (at the touch down point between ground and the line to the airplane)

= 180 - 90 - 32 = 58 degrees.

if we imagine now a circle being drawn with the touch down point being center and going through the right- angle corner point on the ground right under the airplane, we see that the ground distance from that corner to the landing strip is the radius of that circle.

therefore, the height is tan() × r of the angle at the touch down point.

5473 = tan(58) × r

r = 5473 / tan(58) = 3420 m