Question

question
colton is flying a kite, holding his hands a distance of 3 feet above the ground and letting all the kite’s string play out. he measures the angle of elevation from his hand to the kite to be ( 32^circ ). if the string from the kite to his hand is 90 feet long, how many feet is the kite above the ground? round your answer to the nearest hundredth of a foot if necessary.

Explanation:

Step1: Identify vertical height component

We use the sine function to find the vertical distance from Colton's hand to the kite.
$\text{Vertical distance from hand} = 90 \times \sin(32^\circ)$

Step2: Calculate the vertical component

First, compute $\sin(32^\circ) \approx 0.5299$, then multiply by 90:
$90 \times 0.5299 \approx 47.691$

Step3: Add height of hand above ground

Add the 3 feet height of Colton's hands to the vertical distance from hand to kite.
$\text{Total height above ground} = 47.691 + 3$

Answer:

50.69 feet