SOLUTION: You are on a pleasure cruise through the universe and you crash in the ocean of an unknown planet. Your spaceship floats on the water and its top is 34 feet above the surface of th
Question 18891: You are on a pleasure cruise through the universe and you crash in the ocean of an unknown planet. Your spaceship floats on the water and its top is 34 feet above the surface of the water. You swim away from the spaceship until you see its top on the horizon. Your laser range meter tells you that your eyes are 2.2 miles away from the top of the space ship. (You are a capable - if reckless and curious - swimmer.) The radius of the planet is miles. It's a small world, but it's all yours!
You can put this solution on YOUR website! consider a circle with radius x
ther is a point on circumfrence s where the ship is
connect this point to the center of circle o
extend os line to outside of circle to point t
which is the top of the ship
so we have line ost wher os = x and st = 34f
draw a tangent to the circle passing through t and touching the circle
at point k so we have tk as the distance of swimmer from the tip of the ship
which is 2.2 miles = 2.2*5280 feet = 11616 Feet
connect k to center of circle o
u can see a right triangle okt right angled at k
ko = x
kt = 11616
to = x + 35
So ko^2 + kt^2 = to^2
x^2 + 11616^2 = (x + 35)^2
x^2 + 11616^2 = x^2 + 35^2 + 70x
11616^2 = 35^2 + 70x
11616^2 - 35^2 = 70x
134930231 = 70x
x = 134930231/70
= 1927574Feet
= 1927574/5280 miles
= 365 Miles
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