Answer:
26.2655 miles
Step-by-step explanation:
Whenever possible, draw a diagram. I've attached a picture of the balloon and the lines of depression (not drawn to scale, of course).
As you can see, the angles of depression form alternate interior angles with the ground (angles of elevation). So these angles are also 13° and 39°.
We can use the tangents of these angles to find the base lengths of the two triangles that are formed.
tan 13° = 4 / a
a = 4 / tan 13°
tan 39° = 4 / b
b = 4 / tan 39°
So the total distance is:
a + b
= 4 / tan 13° + 4 / tan 39°
≈ 22.2655
