Question

question
aubrey is flying a kite, holding her hands a distance of 2.5 feet above the ground and letting all the kite’s 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.
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Explanation:

Step1: Identify the right triangle

We have a right triangle where the hypotenuse (string length) is 150 feet, the angle of elevation is \(25^\circ\), and we need to find the height from the hand level to the kite, then add the 2.5 feet from hand to ground.

Step2: Calculate height from hand to kite

Using the sine function: \(\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}\). Let \(h\) be the height from hand to kite. So \(\sin(25^\circ)=\frac{h}{150}\). Then \(h = 150\times\sin(25^\circ)\). Calculate \(\sin(25^\circ)\approx0.4226\), so \(h\approx150\times0.4226 = 63.39\) feet.

Step3: Add the hand's height above ground

The hand is 2.5 feet above ground, so total height \(H=63.39 + 2.5=65.89\) feet.

Answer:

65.89