a boy lets out 150 feet of kite string. the string makes an angle of 64 degrees with the ground. his hands hold the reel 3 feet above the ground. assuming the string is straight, how high above the ground is the kite? round to the nearest tenth of a foot

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06-11-2016
Mathematics

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a boy lets out 150 feet of kite string. the string makes an angle of 64 degrees with the ground. his hands hold the reel 3 feet above the ground. assuming the string is straight, how high above the ground is the kite? round to the nearest tenth of a foot

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hooniboi hooniboi · Answer 1 · 2016-11-06T23:55:02+01:00

envision a right triangle with hypotenuse 150 feet, and the opposite angle to the height of the triangle is 64 degrees.
Therefore we can use the trigonometric equation of
sin64 = opposite/hypotenuse
multiply both side of the equation by hypotenuse and we get
hypotenuse(sin 64) = opposite
then the opposite height is 150sin64, which is 134.8
134.8 + 3 = 137.8, because this the triangle should be 3 feet off the ground.
therefore the kite is 137.8 feet off the ground.

hope this helps