SOLUTION: A beautiful blue kite is attached to the back of your boat on a 250 foot string. As the speed of the boat increases, the kite rises into the air. The kite is 200 ft. behind the boa

Question 536494: A beautiful blue kite is attached to the back of your boat on a 250 foot string. As the speed of the boat increases, the kite rises into the air. The kite is 200 ft. behind the boat when the string is taut. What is the height of the kite above the water?
Found 2 solutions by josmiceli, lmeeks54:
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
The string of the kite forms the hypotenuse
of a right triangle with 200 ft as the base
Call the height of the triangle
Use the Pythagorean theorem

The kite is 150 ft above the water
Answer by lmeeks54(111) (Show Source): You can put this solution on YOUR website!
This problem requires understanding right triangles. Take the words out and picture a triangle in which the base = 200 ft (the distance the kite is behind the boat) and the hypotenuse is 250 ft (the length of the string holding the kite). We are left to figure out the other side, which is the height.
...
The basic formula linking the 3 sides of a right triangle is the pythagorean theorem: c^2 = a^2 + b^2, where, c is the hypotenuse, and a and b are the base and height of the triangle. We know c and a, so we need find b, and to do that, we need to rewrite the pythagorean theorem in terms of b:
...
c^2 = a^2 + b^2 is the same as:
c^2 - a^2 = b^2 after subtracting a^2 from both sides
...
flip it around:
b^2 = c^2 - a^2
...
take the Sqrt of both sides:
b = Sqrt(c^2 - a^2)
...
b = Sqrt(250^2 - 200^2)
b = 150
...
The kite is 150 ft above the water
...
Cheers,
Lee
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