You look down at an object on the ground. If your eyes are 55 feet above the ground, and the angle of depression is 50º, how far is the object
from you?

i believe it’s 2,750 feet?

We can think of this as a triangle rectangle.

We know that you eyes are 55ft above the ground, this can be one cathetus.

We also know that you see with an angle of depression of 50°, from this angle, our known cathetus would be the opposite cathetus.

Now we want to know how far is the object from you, this would be the hypotenuse of the triangle rectangle.

So we only know one angle and the opposite cathetus to this angle, then we can use the relation:

Sin(θ) = (opposite cathetus)/(hypotenuse)

Then if we use this equation, we will get:

Sin(50°) = 55ft/hypotenuse

hypotenuse = 55ft/sin(50°) = 71.8 ft

This means that the distance between you and the object is 71.8 ft.