You are flying your dragon kite on 38 yd of string. The kite is directly above the edge of a pond. The edge of the pond is 36 yd from where the kite is tied to the ground. How far is the kite above the​ pond?

The height is approximately

1 answer

To find the height of the kite above the pond, we can use the Pythagorean Theorem. In this scenario, the string of the kite acts as the hypotenuse of a right triangle, where:

  • The height of the kite above the pond is one leg of the triangle (let's call this \( h \)).
  • The distance from the point where the kite is tied to the ground to the edge of the pond is the other leg of the triangle (which is 36 yards).
  • The length of the string (38 yards) is the hypotenuse.

According to the Pythagorean theorem:

\[ h^2 + 36^2 = 38^2 \]

Now we can substitute the values:

\[ h^2 + 1296 = 1444 \]

Next, we subtract 1296 from both sides:

\[ h^2 = 1444 - 1296 \] \[ h^2 = 148 \]

Now, we take the square root of both sides to find \( h \):

\[ h = \sqrt{148} \]

Now, we can simplify \( \sqrt{148} \):

\[ \sqrt{148} = \sqrt{4 \times 37} = 2\sqrt{37} \]

Now we can calculate \( \sqrt{37} \) using a calculator, which is approximately 6.08.

So,

\[ h \approx 2 \times 6.08 \approx 12.16 \text{ yards} \]

Thus, the height of the kite above the pond is approximately 12.16 yards.