Question

aubrey is flying a kite, holding her hands a distance of 2.5 feet above the ground and letting all the kites string play out. she measures the angle of elevation from her hand to the kite to be 25°. if the string from the kite to her hand is 150 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 from hand

We use the sine function to find the vertical distance from Aubrey's hand to the kite, since we know the hypotenuse (string length) and the angle of elevation.
$\text{Vertical height from hand} = 150 \times \sin(25^\circ)$
Calculate $\sin(25^\circ) \approx 0.4226$, so $150 \times 0.4226 = 63.39$ feet.

Step2: Add height of hand to ground

Add the 2.5 feet height of Aubrey's hand above the ground to the vertical height from her hand to the kite.
$\text{Total height above ground} = 63.39 + 2.5$

Answer:

65.89 feet