# Tricky Lighthouse (well, tricky for me (a fool))— Finding Maximum Angle of Elevation

Here's the problem I'm stuck on. I'm honestly not even sure what it's asking.

"The axis of a light in a lighthouse is tilted. When the light points east, it is inclined upward at 1 degree(s). When it points north, it is inclined upward at 2 degree(s). What is its maximum angle of elevation? (Hint: The maximum angle of elevation of plane of the beam above the horizontal plane is the same as the angle between the normal to the plane of the beam and the normal to the horizontal plane.)"

Can anyone help me visualize what I'm trying to solve? Or how I should begin tackling this (probably simple) problem?

Any kind of help will be greatly appreciated. I'll respond as soon as possible.

Thank you

EDIT: I'm going to start working on this here. I may have figured something out. Maybe set the lighthouse at the origin (0,0,0), and have two vectors <0,1,1... degree..? crap nevermind

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## 1 Answer

The problem gives two vectors in the plane perpendicular to the axis of the lighthouse, $(1,0,\tan(1^\circ))$ and $(0,1,\tan(2^\circ))$. To find the axis of the lighthouse, take the cross product. The maximum angle of tilt is the angle of the axis from the vertical $(0,0,1)$.

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I'm sorry for being dense, but I don't understand fully. I can see how you got (1,\tan(1^\circ),0) and (\tan(2^\circ),1,0)... and the cross product would be approximately .99939K Then the direction of the axis would be... K..? I'm still confused, I'm sorry man. Oh wait, you changed the numbers! I'm going to try this again. Alright so the cross product is <-tan(1 degree), -tan(2 degrees), 1> – user13327 Sep 25 '11 at 8:38
I got it! Finally! Thank you! – user13327 Sep 25 '11 at 8:46