SOLUTION: When the sun's angles of elevation is 30degrees the shadow of the post is 6 ft longer then when the angle is 45 degrees . find the height of the post.
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-> SOLUTION: When the sun's angles of elevation is 30degrees the shadow of the post is 6 ft longer then when the angle is 45 degrees . find the height of the post.
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Question 390192: When the sun's angles of elevation is 30degrees the shadow of the post is 6 ft longer then when the angle is 45 degrees . find the height of the post.
Can you please include the work of how the question was answered.
Thank you! Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! When the sun's angle of elevation is 30 degrees the shadow of the post is 6 ft longer then when the angle is 45 degrees . find the height of the post.
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Let the height of the post be "x" ft.
Then the shadow at 45 degrees is "x" ft.
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Shadow at 30 degrees will be x+6 ft.
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You have a 30/60 degree right triangle
with legs x and x+6.
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The hypotenuse will be 2*the side opposite the 30 degree angle.
hypotenuse = 2x
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The hypotenuse will also be sqrt[x^2 + (x+6)^2]
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Solve for "x":
2x = sqrt[x^2 + (x+6)^2]
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4x^2 = x^2 + x^2+12x+36
2x^2-12x-36 = 0
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x^2 - 6x - 18 = 0
x = [6 +- sqrt[36-4*1*-18]/(2)
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Positive solution:
x = [6 + 10.39]/2
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x = 8.195 ft.
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Cheers,
Stan H.
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