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Kaj is flying a kite, holding her hands a distance of 3.5 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
33^(@). If the string from the kite to her hand is 75 feet long, how many feet is the kite above the ground? Round your answer to the nearest hundredth of a foot if necessary.

Kaj is flying a kite, holding her hands a distance of $3$ . $5$ 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 $33^{\circ}$ . If the string from the kite to her hand is $75$ 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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Pythagorean theorem

Full solution

Q. Kaj is flying a kite, holding her hands a distance of

3

.

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

33^{\circ}

. If the string from the kite to her hand is

75

feet long, how many feet is the kite above the ground? Round your answer to the nearest hundredth of a foot if necessary.

Identify Triangle: question_prompt: How high is the kite above the ground?
Use Trigonometry: Identify the right triangle formed by the kite string, the ground, and the line from Kaj's hand to the kite. We'll use trigonometry to solve for the height of the kite above the ground.
Calculate Height: The angle of elevation is $33$ degrees and the string is $75$ feet long. We'll use the sine function since we want to find the opposite side of the angle, which is the height of the kite above Kaj's hand.
Find Sine Value: Calculate the height above Kaj's hand using the sine function: $height = 75 \times \sin(33^\circ)$ .
Perform Multiplication: Use a calculator to find $\sin(33^\circ)$ and multiply by $75$ . $\sin(33^\circ) \approx 0.5446$ . So, height $\approx 75 \times 0.5446$ .
Add Heights: Perform the multiplication: $\text{height} \approx 75 \times 0.5446 \approx 40.845$ feet.
Perform Addition: Add the height of Kaj's hands above the ground to the height of the kite above her hands to get the total height of the kite above the ground. Total height = $40.845$ feet + $3.5$ feet.
Round Answer: Perform the addition: Total height $\approx 40.845 + 3.5 \approx 44.345$ feet.
Round Answer: Perform the addition: Total height $\approx 40.845 + 3.5 \approx 44.345$ feet. Round the answer to the nearest hundredth of a foot: Total height $\approx 44.35$ feet.

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