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The kite problem

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        The Kite Problem


                         Pythagorean Theorem by Leah & Reagan  

A kite is tethered to 500ft of string. A girl is directly under the kite & stands 400ft away from the person flying the kite. How high is the kite? 

Using Pythagorean theorem, a^2 + b^2 = c^2, the c^2 or "the leg" of the triangle, is represented by the string that is 500ft long. The a^2 side of the triangle is represented by the 400ft of that the person is standing away from the person flying the kite. Lastly, the b^2 side of the triangle is the unknown number of how high the kite is above the ground. 400ft^2 + b^2 = 500ft^2. First, we square the numbers and plug them into the equation, which comes out to 160,000ft + b^2 = 250,000ft. Then we subtract the a^2 and the c^2 sides by 160,000ft. This will end up canceling out the 160,000ft side and leaving the equation to b^2 = 90,000ft. Finally, we unsquare the triangle by finding the square root. b = 300ft.

Problem #1

a^2 + b^2 = c^2

400ft^2 + b^2 = 500ft^2

(square the numbers) 

 160,000ft + b^2 =  250,000ft

-160,000ft + b^2 = -160,000ft

(Square root the 90,000ft)    b^2 =  90,000ft 

b = 300ft

Problem #2

While the girl and boy were flying the kite, a big gust of wind blew the kite even higher than it was. The girl estimated that the kite was tethered to 700ft of string. The boy followed the kite that was now 600ft away from the person holding the kite. Now how high was the kite? 

Again, using Pythagorean theorem, a^2 + b^2 = c^2, the new length of the leg of the triangle is 700ft^2. The a^2 side of the triangle is the length between the two people, which is now 600ft apart. The b^2 side of the triangle is still the unknown side of the diagonal. 700ft^2 + b^2 = 600ft^2. First, we will square both numbers and plug them into the equation. 360,000 + b^2 = 490,000. Now, subtract each number by 360,000. By subtracting the 360,000 by itself, it cancels the number out and leaves, b^2 = 130,000ft. Lastly, unsquare the equation by finding the square root of 130,000. We are left with 360.56, and that is the answer to b^2. 

a^2 + b^2 = c^2

600ft^2 + b^2 = 700ft^2

 360,000 + b^2 =  490,000

-360,000 + b^2 = -360,000

                  b^2 =  130,000

(find the square root) 

                  b = 360.56ft



While the boy and girl were watching the magnificence of the kite in the sky, the wind died down; so they wound up some of the tether and saw that the boy and girl were only standing 300ft away from each other. The boy looked up and also saw that the kite was about 150ft up. How much of the string is now tethered to the kite?

The unknown diagonal is now "the leg" of the triangle. The a^2 in this equation is represented by the 300ft^2 of that the boy and girl are standing apart. The b^2 part of the triangle is represented by the height of the kite which is 150ft^2. 300ft^2 + 150ft^2 = c^2. First we square the numbers and plug them into the equation. 90,000ft + 22,500ft = c^2. Now, we add 90,000ft + 22,500ft and end up with 112,500ft. We are now left with 112,500 = c^2, Lastly, we square the 112,500ft and are left with the answer to c^2. c = 335.41. 

Problem #3

a^ + b^2 = c^2

300ft^2 + 150ft^2 = c^2

90,000ft + 22,500ft = c^2

(add them together)

112,500 = c^2

(find the square root) 

c^2 = 335.41ft