Lighthouse question

[FloorLava]

This question could go under trig but also calculus.

We recently got this question in our year 12 Methods class

After a few other questions, which talked of a light at the top of the light house and finding a sin graph from the intensity of light hitting a sensor as the light rotated, the question I can't solve gave the diameter of the bottom of the lighthouse as 8 metres and said there was a road that ran along side the lighthouse on the right from North to South, with the road touching the lighthouse.

With the diagram showing the light facing towards the road, touching the top and bottom corner, at what could be a 90 degree angle, the question asks to write a Tangent equation that models when the light touches the road:

A x Tan(nx)
Solve A and n

The previous question stated that it takes 12 seconds for the light to fully rotate.

 

[stapel]

...the question I can't solve gave the diameter of the bottom of the lighthouse as 8 metres and said there was a road that ran along side the lighthouse on the right from North to South, with the road touching the lighthouse.

With the diagram showing the light facing towards the road, touching the top and bottom corner....

What is "touching the top and bottom corner"? And "touching the top and bottom corner" of what?

...at what could be a 90 degree angle...

Um... In trig, the exact measure of the angle is gonna be kind of important, I think.... :shock:

...the question asks to write a Tangent equation that models when the light touches the road....

That makes no sense. Lighthouses, by definition, shine their lights horizontally, so as to be visible far out to sea. With the road passing alongside (and "touching" the base of) the lighthouse, the light logically can never "touch" ("cross"? "illuminate"?) the road. Maybe they're talking about some other point on the road? Or maybe they're talking about the light beam at some distance away, where maybe the beam has spread enough to reach down to the ground? Either way, though, I don't see how the diameter of the base of the lighthouse would matter...?

Please reply with the full and exact text of the exercise (maybe including the previous part(s), too), the complete instructions, and a scan of the picture (which seems to be required in order to understand what is being asked). When you reply, please include a clear listing of your thoughts and efforts so far. Thank you!