Question

miguel is flying a kite, holding his hands a distance of 3.5 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 25°. if the string from the kite to his hand is 150 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 Miguel's hand to the kite, since $\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}$.
$\text{Vertical height from hand} = 150 \times \sin(25^\circ)$

Step2: Calculate the vertical height

Compute the value using a calculator (ensure it is in degree mode):
$150 \times \sin(25^\circ) \approx 150 \times 0.4226 = 63.39$ feet

Step3: Add height of hand from ground

Add the 3.5 feet height of Miguel's hand above the ground to the vertical height from hand to kite.
$\text{Total height} = 63.39 + 3.5$

Answer:

66.9 feet