SOLUTION: Pythagorean Theorem fun..You are in the crow's nest of a ship that is 40ft. above the water. Determine the farthest distance from which you could spot the top of a 50 ft tree on a

Question 540339: Pythagorean Theorem fun..You are in the crow's nest of a ship that is 40ft. above the water. Determine the farthest distance from which you could spot the top of a 50 ft tree on a sea level island. Earth's radius is 3963 ft. A mile is 5280 ft. I've drawn the mast with the crows nest and labeled it 40 ft. Ive drawn a tree and labeled it 50 ft. I don't see where I'm supposed to get the triangle to figure the Pythagorean Theorem. I know the Earth is curved, but how do I figure that in to this problem?
Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
fun, huh...

the line of sight from the crow's nest (what about your height? 6 feet?) to the top of the tree is tangent to the Earth's surface
___ at the point of tangency, the line is perpendicular to (right angle) the Earth's radius

so you have TWO right triangles, where the sum of the two missing sides is the distance you want to find

the common side of the triangles is the Earth's radius (3963 * 5280)

one hypotenuse is the crow's nest [(3963 * 5280) + 40] ... your height?

the other hypotenuse is the tree top [(3963 * 5280) + 50]

use Pythagoras to find the missing sides (hope you have a lot of digits on your calculator)
___ Windows has a good built-in scientific calculator
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