Shanice measures her shadow at 7 ft 6 in long. She then measures the shadow of the oak tree at 74 ft 3 in long. She also measures the shadow of her house that is 28 ft 6 in. Using this information how much taller is the tree than the house if her actual hight is 5 ft 10 in.
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converting feet to inches!!!
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Re: converting feet to inches!!!
Originally posted by joyllee View PostShanice measures her shadow at 7 ft 6 in long. She then measures the shadow of the oak tree at 74 ft 3 in long. She also measures the shadow of her house that is 28 ft 6 in. Using this information how much taller is the tree than the house if her actual hight is 5 ft 10 in.
7 ft 6 in gives 7*12 + 6 = 90 inches. Do the others the same way,
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Re: converting feet to inches!!!
This problem can be solved through trigonometry or simplified if we assume the angle of sunlight is constant.
First, lets convert all lengths into feet.
Shanice at 5'10'' = 5.8333 ft
Shadow of Shanice at 7'6'' = 7.5 ft
Shadow of house at 28'6'' = 28.5 ft
Shadow of tree at 74'3'' = 74.25 ft
Trigonometry solution:
Draw 3 right triangles to represent the girl, the house, and the tree.
Let x = angle between the length of the shadow and the hypotenuse of the triangle.
x (in degrees) = arctan(5.8333/7.5) = 37.9 degrees
Height of house = 28.5*tan(37.9) = 22.2 ft
Height of tree = 74.25*tan(37.9) = 57.8 ft
Therefore, (height of tree  height of house) = (57.8  22.2) = 35.6 ft, or 35'7''
Simplified solution:
assuming angle of sunlight is constant, the three triangles are considered similar and therefore have constant proportions. This allows us to multiply Shanice's Height/Shadow ratio by the shadow length of the house and tree to determine the heights of the house and tree.
Shanice's height/shadow ratio = 5.8333/7.5 = 0.778 ft/ft of shadow
Therefore the height of the house = 0.778 ft/ft of shadow * 28.5ft of shadow = 22.2 ft
Height of tree = 0.778 * 74.25 ft = 57.8 ft.
Therefore, (height of tree  height of house) = (57.8  22.2) = 35.6 ft, or 35'7''
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