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Part 1
You are flying your dragon kite.​ It's connected to 30 yd of string. The kite is directly above the edge of a pond. The edge of the pond is 27 yd from where the kite is tied to the ground. How high is the kite above the edge of the​ pond?
27 yd
30 yd
​(The figure is not drawn to​ scale.)
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Part 1
The kite is about
  
enter your response here yd above the edge of the pond.
​(Round to one decimal place as​ needed.)

1 answer

To find the height of the kite above the edge of the pond, we can use the Pythagorean theorem. The kite, the ground where the string is tied, and the edge of the pond form a right triangle.

Let's define the triangle's sides:

  • The length of the string is the hypotenuse \( c = 30 \) yd.
  • The distance from where the kite is tied to the edge of the pond is one leg of the triangle \( a = 27 \) yd.
  • The height of the kite above the edge of the pond is the other leg of the triangle \( b \).

According to the Pythagorean theorem:

\[ c^2 = a^2 + b^2 \]

Substituting in the known values:

\[ 30^2 = 27^2 + b^2 \]

Calculating the squares:

\[ 900 = 729 + b^2 \]

Now, isolate \( b^2 \):

\[ b^2 = 900 - 729 \] \[ b^2 = 171 \]

Taking the square root to find \( b \):

\[ b = \sqrt{171} \approx 13.1 \text{ yd} \]

Thus, the kite is about 13.1 yd above the edge of the pond (rounded to one decimal place).