Question

jaxon is flying a kite, holding his hands a distance of 3.25 feet above the ground and letting all the kites string play out. he measures the angle of elevation from his hand to the kite to be 24°. if the string from the kite to his hand is 105 feet long, how many feet is the kite above the ground? round your answer to the nearest tenth of a foot if necessary.

Explanation:

Step1: Identify vertical height component

We use the sine function to find the vertical distance from Jason's hand to the kite. The formula is $\text{Vertical distance} = \text{String length} \times \sin(\text{Angle of elevation})$.
$\text{Vertical distance} = 105 \times \sin(24^\circ)$
Calculate $\sin(24^\circ) \approx 0.4067$, so $105 \times 0.4067 \approx 42.7035$ feet.

Step2: Add height of Jason's hand

Add the 3.25 feet height of Jason's hand above the ground to the vertical distance found.
$\text{Total height} = 42.7035 + 3.25$

Step3: Compute final height

Perform the addition and round to the nearest tenth.
$\text{Total height} \approx 45.9535 \approx 46.0$ feet

Answer:

46.0 feet