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A boy who is flying a kite lets out 270 feet of string which makes an angle of 60° with the ground. Assuming that the string is stretched out in the boys sitting on the ground, find, to the nearest foot, how high the kite is above the ground?

User Dogs
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1 Answer

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Final answer:

To find the height of the kite, use the sine function with the given string length and angle. The height is the product of the string length and the sine of the angle, which is sin(60°), giving the final height to the nearest foot after calculation.

Step-by-step explanation:

The question involves finding the height of a kite above the ground given the length of the string and the angle the string makes with the ground. This can be solved using trigonometry, specifically the sine function, since we are given the hypotenuse (the string) and need to find the opposite side (the height of the kite). The sine of an angle in a right triangle is equal to the length of the opposite side divided by the length of the hypotenuse. Here, we use the formula:

height = string length × sin(angle)

Substituting the given values:

height = 270 feet × sin(60°)

Calculating the sine of 60° (which is √3/2) and then multiplying it by 270 feet:

height = 270 feet × (√3/2)

To the nearest foot, the height of the kite can be rounded off after computation.

User Tsturzl
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