# Find the angle of depression

I am having trouble solving this word problem:

A cellular tower that is 150ft is placed on top of a mountain that is 1200 feet above sea level. what is the angle of depression from the top of the tower to a cell phone user who is 5 horizontal miles away and 400 feet above sea level?

Here is my attempt:

-opposite side = 5 miles = 26400ft

so: tan(?) = (26400ft / 950ft), arctan should give us the angle.

arctan(26400ft/950ft) = 87.94 degrees. this angle is the one with mountain and a slope to the head of user. Thus an angle of depression as it is an angle formed between horizontal line and that slope which is equal to 90 degree -87.94 degrees=2.06 degrees

What am I doing wrong?

Here is a sketch of the problem I made, did I interpret it wrong?

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Notice that your answer and the text's answer sum to 90 degrees. The text wants a different, but related, angle from the one you found. – Matthew Conroy Apr 20 '11 at 23:23
So that would be the angle of elevation though, not the angle of depression, wouldn't it? – Matt Apr 20 '11 at 23:28
I think 2.06 degrees is a reasonable description of how depressed the cell phone user's position is from the horizontal line at the top of the cell tower. Your method is absolutely sound: just subtract your result from 90 degrees to get the desired angle. The 87.94 degree angle doesn't measure how elevated anything is, so I wouldn't use the term "angle of elevation" for it, myself. – Matthew Conroy Apr 20 '11 at 23:36
I quote from www.mathwords.com because I am not a native English speaker: "Angle of Depression The angle below horizontal that an observer must look to see an object that is lower than the observer." mathwords.com/a/angle_depression.htm – Américo Tavares Apr 20 '11 at 23:41