A man flies a kit and lets out 100 feet of string. The angle of elevation of the string is 52°. How high off the ground is the kite? O 78 feet O 110 feet O 75 feet 52 feet
A man flies a kit and lets out 100 feet of string. The angle of elevation of the string is 52°. How high off the ground is the kite? O 78 feet O 110 feet O 75 feet 52 feet
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
![A man flies a kite and lets out 100 feet of string. The angle of elevation of the string is 52°. How high off the ground is the kite?
Options:
- 78 feet
- 110 feet
- 75 feet
- 52 feet
In this problem, you can use trigonometry to find the height of the kite. The string forms the hypotenuse of a right triangle, the height off the ground is the opposite side, and the angle of elevation is 52°. You can use the sine function, as sine is the ratio of the opposite side to the hypotenuse.
Formula:
\[ \text{Sine of angle} = \frac{\text{Opposite side}}{\text{Hypotenuse}} \]
\[ \sin(52°) = \frac{\text{Height}}{100} \]
Now, solve for the height:
\[ \text{Height} = 100 \times \sin(52°) \]
Calculate to find which option represents the height of the kite.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F45e4ee6c-a715-4803-9fbe-92a41a442b45%2Fade12725-0222-4cb6-a30e-a368d0937388%2Fviitgd_processed.jpeg&w=3840&q=75)
Transcribed Image Text:A man flies a kite and lets out 100 feet of string. The angle of elevation of the string is 52°. How high off the ground is the kite?
Options:
- 78 feet
- 110 feet
- 75 feet
- 52 feet
In this problem, you can use trigonometry to find the height of the kite. The string forms the hypotenuse of a right triangle, the height off the ground is the opposite side, and the angle of elevation is 52°. You can use the sine function, as sine is the ratio of the opposite side to the hypotenuse.
Formula:
\[ \text{Sine of angle} = \frac{\text{Opposite side}}{\text{Hypotenuse}} \]
\[ \sin(52°) = \frac{\text{Height}}{100} \]
Now, solve for the height:
\[ \text{Height} = 100 \times \sin(52°) \]
Calculate to find which option represents the height of the kite.
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