Question

question
luis is flying a kite, holding his hands a distance of 3.75 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 35°. if the string from the kite to his hand is 140 feet long, how many feet is the kite above the ground? round your answer to the nearest tenth of a foot if necessary.
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Explanation:

Step1: <Find the height from hand>

We use the sine function. The formula is \(h = l\times\sin\theta\), where \(l = 140\) (length of string) and \(\theta=35^{\circ}\). So \(h = 140\times\sin(35^{\circ})\).
Since \(\sin(35^{\circ})\approx0.5736\), then \(h = 140\times0.5736 = 80.304\).

Step2: <Find the total height>

The total height \(H\) is the height from hand plus the height of hands above ground. \(H=h + 3.75\).
Substitute \(h = 80.304\) into the formula: \(H=80.304+3.75=84.054\approx84.1\).

Answer:

\(84.1\) feet