Trigonometry: Finding the lengths of a right triangle I am currently working on a problem that was on a test of mine that I took recently.  I got the result back and am working on test corrections to make my grade better! But, I am currently stuck on a problem so I thought I would seek help. Before telling the question and what I have been doing I need to say that I am in High School and this is part of my Honors Pre-calculus class. And I am just starting to learn about trigonometry. Alright here is the question!

A tourist looks out from the observation deck of the Space Needle in Seattle. The deck is at a height of 520 feet. She sees her friend on the ground below at an angle of depression of 85.6 degrees. What is the distance between the two? Round your answer to the nearest tenth of a foot. 

From taking the test I know the correct answer is 521.5 ft. Here is what I did on the test: Click here for my work
I am really stuck and I do not know what to do not know what to do. Some help would would be really appreciated. Thanks in advance! 
 A: You're construing "angle of depression" incorrectly. The angle of depression is how far the direction is below the horizontal, not how far it is above the vertical.
A: In your answer, you seem to be confused about the angle. The figure looks like this (I'm not drawing to scale, by intention.)

The tourist is at $A$, the friend $C$, and the problem tells you $\beta=85.6^\circ$. The key insights are then (1) clarifying whether "distance" refers to the direct fly distance AC or the ground distance BC; this is not clear to me from your post (2) recognizing that $\alpha=\beta$ and then invoking the appropriate trig relation based on your definition of "distance".
If the tourist gets down to the bottom of the observation tower, then travels on ground to the friend, then "distance" $d$ ($=BC$) satisfies
$$
520/d = \tan(\alpha)=\tan(85.6^\circ)\implies d=40.0118.
$$
If the tourist can fly directly to the friend, then "distance" $d$ ($=AC$) satisfies
$$
520/d=\sin(\alpha)=\sin(85.6^\circ)\implies d=521.537.
$$
Given the answer, the teacher intended the latter but, in my opinion, the question is ambiguous.
