Question

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

Answer 1

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**.