# Finding the height given the angle of elevation and depression.

Please, I need help for this problem. I'm a little confused about it :(

From a point A 10ft. above the water the angle of elevation of the top of a lighthouse is 46 degrees and the angle of depression of its image is 50 degrees. Find the height of the lighthouse and its horizontal distance from the observer.

I don't know where to start, because the problem doesn't have opposite, hypotenuse, or adjacent side written on it, and I think I cannot use TOA since there were no "Adj" or "Opp" side on the problem.

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It looks like you can set up two equations in two unknowns here. Let $x$ be the lighthouse's height and $y$ be the distance to the lighthouse. Then if the picture in my head is right, $x-10$ and $y$ are the opposite and adjacent sides to a $46^\circ$ angle, and $x+10$ and $y$ are the opp. and adj. sides to a $50^\circ$ angle. – Eugene Shvarts Jul 9 '12 at 8:36

Write EG in terms of angle $50^\circ$.Find $x$. Then the height will be $x\tan 46^\circ + 10$
Let $h$ be the height, $d$ the horizontal distance. Then you arrive at two equations (why?): $$d\tan 46^o=h-10$$$$d\tan 50^o=h+10$$.