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Math Help - Equilateral Triangle

  1. #1
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    Equilateral Triangle

    How long is the largest equialteral trangle that can be inscribed in a square with side length of 1?
    I had intially thought 1, but others told me I was wrong.
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  2. #2
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    Hello, ceasar_19134!

    How long is the largest equialteral trangle
    that can be inscribed in a square with side length of 1?

    The triangle can be inscribed like this . . .
    Code:
          *-----------------*
          |*    *           |
          | *         *     |
          |  *              *
        1 |   * x         * |
          |    *        *   |
          |     * 60 *     |
          |  75 *  * 45   |
          *-------*---------*

    Let x = side of the equilateral triangle.

    In the lower-left right triangle, we have; .sin75 = 1/x

    Hence: .x .= .1/sin75 .= .1.03527615

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