To find the angle of elevation of the kite, we can use trigonometry. Specifically, we will use the sine and cosine functions, but in this case, it's more straightforward to use the tangent function, which is defined as the ratio of the opposite side to the adjacent side in a right triangle.
In this scenario:
- The height of the kite above the ground (opposite side) is 50 meters.
- The length of the string (hypotenuse) is 80 meters.
We need to find the angle of elevation \( \theta \) that the string makes with the ground. We can use the following relation:
\[ \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{50}{80} \]
Now, we'll calculate \( \sin(\theta) \):
\[ \sin(\theta) = \frac{50}{80} = \frac{5}{8} = 0.625 \]
To find the angle \( \theta \), we take the inverse sine (arcsin) of 0.625:
\[ \theta = \arcsin(0.625) \]
Using a calculator to find \( \theta \):
\[ \theta \approx 38.68^\circ \]
Therefore, the angle of elevation of the kite is approximately \( 38.68^\circ \).
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