Question

fawzia is flying a kite, holding her hands a distance of 3.75 feet above the ground and letting all the kites string out. she measures the angle of elevation from her hand to the kite to be 33°. if the string from the kite to her hand is 110 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: Find the vertical height from hand to kite

We use the sine function: $\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$. Here, $\theta = 33^\circ$, hypotenuse (string length) = 110 feet. So the vertical height $x$ from hand to kite is $x = 110 \times \sin(33^\circ)$.
Calculating $\sin(33^\circ) \approx 0.5446$, so $x \approx 110 \times 0.5446 = 59.906$ feet.

Step2: Add the height of hand above ground

The hand is 3.75 feet above ground. So total height of kite above ground is $59.906 + 3.75 = 63.656$ feet. Rounding to nearest tenth gives 63.7 feet.

Answer:

63.7