Question

a kite is flying at a height of 50 meters, the string of the kite makes an angle with the ground. if the length of the string is 70 meters, what angle does the string make with the ground?

Answer 1

To find the angle that the string of the kite makes with the ground, we can use trigonometry. Specifically, we can use the sine function, which relates the angle to the opposite side (the height of the kite) and the hypotenuse (the length of the string).

Let:
- \( h = 50 \) meters (height of the kite)
- \( L = 70 \) meters (length of the string)
- \( \theta \) = angle the string makes with the ground

Using the sine function:

\[
\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{h}{L}
\]

Substituting the known values:

\[
\sin(\theta) = \frac{50}{70} = \frac{5}{7}
\]

Now, we can find the angle \( \theta \) using the inverse sine function:

\[
\theta = \sin^{-1}\left(\frac{5}{7}\right)
\]

Calculating this:

\[
\theta \approx \sin^{-1}(0.7143) \approx 45.57^\circ
\]

Thus, the angle that the string makes with the ground is approximately \( 45.57^\circ \).