# Math Help - angle of depression

1. ## angle of depression

a weather satellite is traveling in a circular orbit 9800 miles above the surface of the earth. find the angle of depression from the satellite to the horizon. assume the radius of the earth is 4000 miles.

i don't get how to find it. i tried finding the angle of angle 1 by using sin. did arcsin and got an angle of 16.85, subtracted it from 90 and got 73 degrees. i thought that was the angle of depression but the book says the answer is 15.5 degrees.

2. Originally Posted by algebra2
a weather satellite is traveling in a circular orbit 9800 miles above the surface of the earth. find the angle of depression from the satellite to the horizon. assume the radius of the earth is 4000 miles.

i don't get how to find it. i tried finding the angle of angle 1 by using sin. did arcsin and got an angle of 16.85, subtracted it from 90 and got 73 degrees. i thought that was the angle of depression but the book says the answer is 15.5 degrees.
that is the angle of depression. (not angle 2 in your diagram--where did that diagram come from).

was a diagram given with the problem?

3. yeah, that is the diagram.

angle 2 is the angle of depression. i used angle 1 to find angle 2 because i thought angle 1 + angle 2 = a right angle.

so i thought i would find angle 1, then subtract it from 90 degrees to find angle 2 (angle of depression)

4. Originally Posted by algebra2
yeah, that is the diagram.

angle 2 is the angle of depression. i used angle 1 to find angle 2 because i thought angle 1 + angle 2 = a right angle.

so i thought i would find angle 1, then subtract it from 90 degrees to find angle 2 (angle of depression)
you are right.

though i would measure the angle of depression "above" angle one, as you see in this diagram

but still, the answer is way-off from the one in the book. either this is a major typo, or that is not the diagram to use...

5. this is the book's solution

6. Originally Posted by algebra2

this is the book's solution
yes, that is the angle i was talking about. the angle you mark as angle 2 in your diagram is not the angle of depression

anyway, it is the hypotenuse of the triangle that is different from yours. i wonder where they got 4150 from? ...