How far is the Object?

greatwhiteshark

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May 8, 2005
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The top of a lighthouse is 230 feet above the sea. How far away is an object which is just "on the horizon"? [Assume the earth is a sphere of radius 3956 miles.]
 
greatwhiteshark said:
The top of a lighthouse is 230 feet above the sea. How far away is an object which is just "on the horizon"? [Assume the earth is a sphere of radius 3956 miles.]
Did you draw a picture?

Draw a circle.
Draw two radii, not too far apart.
Extend one radius a little outside the circle.
From that extension, draw a line segment tangent to the circle at the other radius.
Lable the angle at the tangent, 90º.
Lable the radius to the tangent, 3956 mi
Lable the extended radius, 3956 mi + 230 ft.

Fix the units inconsistencies.
Think about the Pythagorean Theorem.

Do you know that part of the study of mathematics is learning how to think, learning how to deal with abstract concepts, and learning how to decode situations and reduce them to arithmetic. If you are still trying to learn "the trick" to each problem type, you are in for a VERY LONG voyage through very little mathematics. Example after example after example will not do the trick. You have to start thinking on your own or you are fighting a losing battle.
 
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