SOLUTION: The base is a 30, 60, 90 degree triangle with a hypotenuse of 14m. The height of the prism is 11m. Find the volume to the nearest tenth.

Algebra ->  Triangles -> SOLUTION: The base is a 30, 60, 90 degree triangle with a hypotenuse of 14m. The height of the prism is 11m. Find the volume to the nearest tenth.       Log On


   

Question 595637: The base is a 30, 60, 90 degree triangle with a hypotenuse of 14m. The height of the prism is 11m. Find the volume to the nearest tenth.

Answer by math-vortex(648) About Me  (Show Source):
You can put this solution on YOUR website!
Hi, there--
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We can find the volume of the triangular prism by finding the area of the triangle base and multiplying by the height of the prism.
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[I] Find the area of the triangle base.
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We know that we have a 30-60-90 degree triangle with a hypotenuse of 14m. We need to find the base and height of this triangle in order to find its area. (This is NOT the same as the height of the prism.)
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You may have learned about the relationship between the side lengths of a 30-60-90 triangle. The shorter leg is half the length of the hypotenuse. The longer leg is the length of the hypotenuse times (1/2)(sqrt(3)). If you do not understand why this is the case, please email me and I'll explain further.
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Let's have the shorter leg be the base B and the longer leg be the height H. You can set this up either way; the area will be the same.
B=%281%2F2%29%2814%29
B=7
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H=%2814%29%28%28sqrt%283%29%29%2F2%29
H=%287%29%28sqrt%283%29%29
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Now let's find the area of the triangle.
A=%281%2F2%29%28B%29%28H%29
A=%281%2F2%29%287%29%287%29%28sqrt%283%29%29
A=%2824.5%29%28sqrt%283%29%29
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[II] Find the volume of the prism. The volume of the prism is the area of the triangle A times the height of the prism, 11m.
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V=%2811%29%28A%29
V=%2811%29%2824.5%29%28sqrt%283%29%29%7D%7D%0D%0A%7B%7B%7BV=%28269.5%29%28sqrt%283%29%29
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This is an exact answer for the volume of the prism. Since sqrt(3) is an irrational number, we cannot represent it exactly as a decimal. However, it is approximately 1.73. This means that the volume of the prism is approximately 466.8m.
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Hope this helps! Feel free to email me if you have questions about my explanation.
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Ms.Figgy
math.in.the.vortex@gmail.com