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Luis is flying a kite, holding his hands a distance of 3.753.75 feet above the ground and letting all the kite’s string play out. He measures the angle of elevation from his hand to the kite to be 35∘35^\circ. If the string from the kite to his hand is 140140 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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Q. Luis is flying a kite, holding his hands a distance of 3.753.75 feet above the ground and letting all the kite’s string play out. He measures the angle of elevation from his hand to the kite to be 35∘35^\circ. If the string from the kite to his hand is 140140 feet long, how many feet is the kite above the ground? Round your answer to the nearest tenth of a foot if necessary.
  1. Identify values, function: Identify the known values and the trigonometric function to use.\newlineWe know the length of the string (hypotenuse) is 140140 feet, the angle of elevation is 3535 degrees, and Luis's hand is 3.753.75 feet above the ground. We need to find the height of the kite above the ground. We will use the sine function because we have the opposite side (height of the kite above Luis's hand) and the hypotenuse.
  2. Set up equation: Set up the equation using the sine function. sin⁡(35∘)=height of the kite above Luis’s hand140 feet\sin(35^\circ) = \frac{\text{height of the kite above Luis's hand}}{140 \text{ feet}}
  3. Solve for height: Solve for the height of the kite above Luis's hand. \newlineheight of the kite above Luis's hand = sin⁡(35∘)×140\sin(35^\circ) \times 140 feet
  4. Calculate sine, multiply: Calculate the sine of 3535 degrees and multiply by 140140 feet.\newlineUsing a calculator, we find that sin⁡(35∘)≈0.5736\sin(35^\circ) \approx 0.5736 (rounded to four decimal places).\newlineheight of the kite above Luis's hand ≈0.5736×140\approx 0.5736 \times 140 feet
  5. Perform multiplication: Perform the multiplication to find the height of the kite above Luis's hand.\newlineheight of the kite above Luis's hand ≈0.5736×140 feet≈80.304 feet\approx 0.5736 \times 140 \text{ feet} \approx 80.304 \text{ feet}
  6. Add heights: Add the height of Luis's hands above the ground to the height of the kite above Luis's hand to find the total height of the kite above the ground.\newlinetotal height of the kite above the ground == height of the kite above Luis's hand ++ height of Luis's hands above the ground\newlinetotal height of the kite above the ground ≈80.304\approx 80.304 feet ++ 3.753.75 feet
  7. Perform addition: Perform the addition to find the total height of the kite above the ground. \newlinetotal height of the kite above the ground ≈80.304\approx 80.304 feet + 3.753.75 feet ≈84.054\approx 84.054 feet
  8. Round answer: Round the answer to the nearest tenth of a foot. total height of the kite above the ground ≈84.1\approx 84.1 feet

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