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7 November, 15:08

An equilateral triangle has a side length of 10 inches. find the length of the triangle altitude

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  1. 7 November, 15:57
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    An equilateral triangle has all side lengths the same, and all angles are 60 degrees. Using this we can split the triangle along its altitude to get two right triangles with a hypotenuse of length 10 and a base of 1/2 of the original length, so 5. Now we can either use the Pythagorean theorem (a^2+b^2=c^2) or the fact that it is a 30 60 90 triangle (angles measure at 30 60 and 90 degrees) Pythagorean theorem is probably easier.

    It stated that the squares of the two legs of a right triangle add to the square of the hypotenuse. So a (the altitude) ^2+5 (the base) ^2=10 (the hypotenuse) ^2

    A^2+5^2=10^2

    A^2+25=100

    A^2=75

    A=sqrt (75)

    A=5*sqrt (3)

    Final answer:

    The altitude of an equilateral triangle with side length 10 is 5sqrt (3), or about 8.66
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