Question

Your kite is stuck in a tree that is 45 feet tall. The angle your string makes with the ground is 68º. 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

48.5 feet

1) Sketching this we have:

2) As the point here is how much string was left out, then let's use a trigonometric ratio to find out that hypotenuse since height is always perpendicular (90º with the ground).

`\begin{gathered} \sin (68)=\frac{opposite}{\text{hypotenuse}}=(45)/(x) \\ \sin (68)=(45)/(x) \\ x\sin (68)=45 \\ (x\sin(68))/(\sin(68))=(45)/(\sin (68)) \\ x=48.53\approx48.5 \end{gathered}`

3) Hence, that kite's string is 48.5 feet long