SOLUTION: how do you find the length of an altitude if you already have the length of all sides?

Question 613487: how do you find the length of an altitude if you already have the length of all sides?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
how do you find the length of an altitude if you already have the length of all sides?
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Sketch a triangle with a base = 10 and sides 6 and 7
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Draw an altitude from the vertex opposite the base to the base.
That is an altitude (h).
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The base now has 2 segments: x and 10-x
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Use Pythagoras to get:
x^2 + h^2 = 6^2
(10-x)^2 + h^2 = 7^2
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Subtract and solve for "x":
(10-x)^2-x^2 = 7^2 -6^2
100-20x = 13
20x = 87
x = 87/20
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Simplify that and substitute into x^2 + h^2 = 6^2 to solve for "h":
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Cheers,
Stan H.

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