Question

Your Kite is stuck in a tree that is 30 feet tall. The angle your string makes with the ground is 63º. Rather than worrying about the kite, you decide to calculate how much string you have let out. Assuming the string is held tight and makes a straight line to the ground, how much string have you let out?

Answer 1

The diagram below represents the situation,

Observe that the string acts as the hypotenuse of the triangle, while the tree acts as the height of the triangle.

We know that the trigonometric function 'sine' relates the angle to the hypotenuse and base. So it is better to apply sine function here,

`\begin{gathered} \sin 63^(\circ)=\frac{30}{\text{String Length}} \\ \text{String Length}=\frac{30}{\text{sin }63^(\circ)} \\ \text{String Length}=33.67 \end{gathered}`

Thus, the length of the string let out is 33.67 feet approximately.