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Math Help - Pythagorean Theorem - College Algebra

  1. #1
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    Pythagorean Theorem - College Algebra

    An equilateral triangle is shown below.



    a.) Find an expression for its height h in terms of a.


    Ok, I have the solution, but I don't understand it. This is how the solutions manual shows it is solved:

    step #1: h^2 + (a/2)^2 = a^2
    a^2 + b^2 = c^2 Pathagorean formula, ok I understand this.

    step #2: h^2 + [(a^2) / 4] = a^2
    a divided by 2 squared equals a squared over 4. Got it.

    step #3: h^2 = (3a^2) / 4
    Ok this is where I'm lost. Where did the 3 times a squared come from?

    step #4: h = [(3a^2) /4]^(1/2)
    I understand this except I still don't know where the 3a^2 came from. h equals the square root of, 3 times a squared divided by 4.

    step #5: h = (a/2)(3^(1/2))
    I understand this as well. a divided by 2, times the square root of 3.
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  2. #2
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    For step 3, they divided the a^2 on the right of the equation by 4 to get a common denominator with the other a^2.
    They then moved the \frac{a^2}{4} to the side with \frac{4a^2}{4}.
    4a^2 - 1a^2= 3a^2
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  3. #3
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    Thanks a lot; this makes perfect sense now.
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