Cherry is flying a kit that is 27 meters above the ground. The angle formed with the string and the ground is 39°. How long is the string? Write the equation and solve using trigonometric functions and showing all of your work to support your answer. Round your answer to the nearest tenth.
To solve this problem, we can use trigonometric functions to find the length of the string. Let's denote the length of the string as \( x \).
We can see that the opposite side is 27 meters and the hypotenuse is \( x \) meters. Since we are given an angle, we can use the sine function:
\[ \sin(39^\circ) = \frac{27}{x} \]
\[ \frac{27}{x} = \sin(39^\circ) \]
\[ x = \frac{27}{\sin(39^\circ)} \]
Let's plug in the values and solve for \( x \):
\[ x = \frac{27}{\sin(39^\circ)} \]
\[ x = \frac{27}{0.6293} \]
\[ x \approx 42.9 \text{ meters} \]
Therefore, the length of the string is approximately 42.9 meters.