Question

John let out 50 foot of kite string when he observes that his kite is directly above a point on the ground 30 feet away from him, how high is the kite ?
Responses
A 35 ft35 ft
B 37 ft37 ft
C 40 ft40 ft
D 45 ft45 ft
E 47 ft

Answer 1

To determine the height of the kite, we can use the Pythagorean theorem. According to the situation, we have:

- The length of the kite string as the hypotenuse (c) = 50 feet
- The horizontal distance from John to the point directly below the kite (one leg of the triangle, a) = 30 feet
- The height of the kite (the other leg of the triangle, b) is what we are trying to find.

According to the Pythagorean theorem:

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

Substituting the known values into the equation:

\[
30^2 + b^2 = 50^2
\]

This simplifies to:

\[
900 + b^2 = 2500
\]

Now, subtract 900 from both sides:

\[
b^2 = 2500 - 900
\]
\[
b^2 = 1600
\]

Now, take the square root of both sides to solve for \(b\):

\[
b = \sqrt{1600} = 40
\]

So, the height of the kite is **40 feet**.

The correct response is **C: 40 ft**.