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 point)

Question

Responses

45.57°45.57 degrees

15.57°15.57 degrees

25.57°25.57 degrees

35.57°35.57 degrees

Answer 1

To find the angle that the string makes with the ground, we can use the sine function. The sine of the angle θ is defined as the ratio of the opposite side to the hypotenuse in a right triangle.

In this case:

• The height of the kite (opposite side) is 50 meters.
• The length of the string (hypotenuse) is 70 meters.

Using the sine function:

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

Calculating this gives:

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

Now, to find the angle θ, we take the inverse sine (arcsin):

\[ θ = \arcsin(0.7143) \]

Using a calculator to find the angle:

\[ θ \approx 45.57° \]

Thus, the angle that the string makes with the ground is approximately 45.57 degrees.