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. Enter only the number.

(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.)

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. Enter only the number.

(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.)

anonymous · Answer

attachment

anonymous · Answer

Please I need help with this. I have no idea where to begin.

anonymous · Answer

It's trig.  Begin with a picture.

wolf1728 · Answer

Wow - that attachment doesn't help at all. The chart makes it look as if Line AL is at least a thousand miles. From other sources, it seems the horizon appears at about 14.3 miles. Greater distances are achieved because of the height of the observer or the height of what is being observed. ************************************************************************** The following information was obtained from this site: http://www.sailnet.com/forums/her-sailnet-articles/21020-light-lists-lighthouses-visible-ranges.html A light's geographic range depends upon the height of both the light and the observer. You can calculate the observer's distance to the horizon based on his height of eye and the light's geographic range. For example, for a light 150 feet above the water, Table 12 (Table 8 in the older Bowditch), Distance of the Horizon, in Bowditch yields a value of 14.3 nautical miles. Within this range, if the light is powerful enough and atmospheric conditions permit, it is visible regardless of the height of eye of the observer. BEYOND 14.3 nautical miles, the geographic range depends upon the observer's height of eye. Thus, by the Distance of the Horizon table, an observer with height of eye of five feet can see the light on his horizon if he or she is 2.6 miles beyond the horizon of the light. The geographic range of the light is therefore 2.6 + 14.3 or 16.9 miles. For a height of 30 feet, the distance is 6.4 + 14.3 or 20.7 miles. *********************************************************************** No trig calculations or anything, but I hope that helps somewhat.

goformit100 · Answer

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