Finding the height given the angle of elevation and depression.

$\begingroup$

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.

$\endgroup$ 1

2 Answers

$\begingroup$

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

$\endgroup$ 0 $\begingroup$

Let $h$ be the height, $d$ the horizontal distance. Then you arrive at two equations (why?): $$d\tan 46^o=h-10$$$$d\tan 50^o=h+10$$.

$\endgroup$ 0

Your Answer

Sign up or log in

Sign up using Google Sign up using Facebook Sign up using Email and Password Submit

Post as a guest

Post Your Answer Discard

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy