Geometry and Measurement

I am trying to solve the length of the hypotenuse of a right triangle with sides of 6mm and 8mm

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  1. For a right angle triangle the following equation is true:

    a^2 + b^2 = c^2

    Where c is the hypotenuse of the triangle and a,b are the other sides (you decide which side is a and which side is b).

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  2. This involves the pythagorean theorem. Let c = hypotenuse; a = 1 side; b = other side.

    c^2 = a^2 + b^2

    c^2 = 6^2 + 8^2
    c^2 = 36 + 64

    Solve for c.

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    Ms. Sue
  3. I am trying to solve the length of the hypotenuse of a right triangle with sides of 6mm and 8mm

    a = 6mm, b = 8mm

    For b > a
    c = b^2[1 + a^2/b^2]/sqrt(a^2 + b^2)

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  4. Regarding:
    For b > a
    c = b^2[1 + a^2/b^2]/sqrt(a^2 + b^2)

    I forgot to acknowledge that when this expression is multipied out, the end result is c = sqrt(a^2 + b^2).

    I was initially surprised when deriving it from the relationship between the altitude to the hypotenuse and the hypotenuse itself;

    * The altitude to the hypotenuse of a right triangle is the geometric mean between the segments of the hypotenuse created by the point where the altitude intersects the hypotenuse or h^2 = xy.

    * With an altitude drawn to the hypotenuse of a right triangle, each leg is the geometric mean between the hypotenuse and the segment of the hypotenuse in contact with the leg.

    Can't beat old Pythagorus.

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