[Math] Finding the height given the angle of elevation and depression.

trigonometry

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.

Best Answer

image
BF is the ground level.
Write EG in terms of angle $50^\circ$.Find $x$. Then the height will be $x\tan 46^\circ + 10$