Question

jordan is flying a kite, holding his hands a distance of 2.5 feet above the ground and letting all the kite’s string 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 hundredth of a foot if necessary.

Explanation:

Step1: Identify opposite side of angle

We use the sine function to find the vertical height \(x\) from Jordan's hand to the kite, since \(\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}\).
\(\sin(24^\circ) = \frac{x}{105}\)

Step2: Solve for vertical height \(x\)

Rearrange the formula to solve for \(x\) and calculate its value.
\(x = 105 \times \sin(24^\circ) \approx 105 \times 0.4067 = 42.7035\)

Step3: Add hand height to ground

Add the height of Jordan's hands above the ground to \(x\) to get the total height of the kite.
\(\text{Total Height} = 42.7035 + 2.5\)

Answer:

45.20 feet (rounded to the nearest hundredth)