Question

The range of a lighthouse is the maximum distance at which its light is visible. In the figure, point A is the farthest point from which it is possible to see the light at the top of the lighthouse L. The distance along Earth, s, is the range. Assuming that the radius of the Earth is 4000 miles, find the range of Marblehead Lighthouse to the nearest tenth of a mile.

Answer 1

iam really stuck on this problem..

Answer 2

Is there a pic.?

Answer 3

nope :(

Answer 4

(Hint: Notice the right triangle EAL with right angle A. Find the length EL, then subtract the radius of the Earth to find the height of the lighthouse.)

Answer 5

Is it like this?

Answer 6

the picute i saw only had like 4000 mi

Answer 7

and i was between a and e

Answer 8

Yes, it's 4000 mi between E and any point on the surface of the earth.

The length of EL will be 4000 between the center and the surface plus a little more for the height of the lighthouse. It will barely matter, since the lighthouse will not be anywhere close to 4000 miles, but on the other hand, if the lighthouse wasn't there, a light shined tangent to the earth would (theoretically) have 0 range...

Answer 9

It just seems like you need to know the height of the lighthouse to solve for the range, s.

The range s depends completely on the height... that's why they build tall antenna towers for communications like radio, cellular, TV, etc... tall towers mean more range.

Answer 10

you get hard problems... :)