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?

1 answer

To find the angle \(\theta\) that the string makes with the ground, we can use the properties of a right triangle.

In this scenario, we have:

  • The height of the kite (the vertical side of the triangle) = 50 meters
  • The length of the string (the hypotenuse of the triangle) = 70 meters

Using the sine function, we can express the relationship as follows:

\[ \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{50}{70} \]

Calculating \(\frac{50}{70}\):

\[ \sin(\theta) = \frac{50}{70} = \frac{5}{7} \approx 0.7143 \]

Now, we take the inverse sine (arcsine) to find \(\theta\):

\[ \theta = \arcsin\left(\frac{5}{7}\right) \]

Using a calculator to find the angle:

\[ \theta \approx 45.57^\circ \]

Thus, the angle that the string makes with the ground is approximately:

\[ \boxed{45.57^\circ} \]