Question

kaj is flying a kite, holding her hands a distance of 3.5 feet above the ground and letting all kites string out. she measures the angle of elevation from her hand to the kite to be 29°. if string from the kite to her hand is 130 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: Use the sine function

In a right - triangle, \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, \(\theta = 29^{\circ}\) and the hypotenuse is the length of the string \(130\) feet. Let the height from her hand level to the kite be \(x\). So, \(\sin(29^{\circ})=\frac{x}{130}\).

Step2: Solve for \(x\)

Multiply both sides of the equation \(\sin(29^{\circ})=\frac{x}{130}\) by \(130\). We get \(x = 130\times\sin(29^{\circ})\). Since \(\sin(29^{\circ})\approx0.4848\), then \(x=130\times0.4848 = 63.024\) feet.

Step3: Find the total height of the kite above the ground

The total height \(h\) of the kite above the ground is the sum of the height from her hand level to the kite (\(x\)) and the height of her hand above the ground (\(3.5\) feet). So, \(h=x + 3.5\). Substitute \(x = 63.024\) into the equation: \(h=63.024+3.5\).

Answer:

\(h = 66.52\) feet.