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Math Help - Help me with thisㅠㅠ(right triangles)

  1. #1
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    Help me with thisㅠㅠ(right triangles)

    Please solve this following problems.^^*

    Find the sides of the [30-60-90] right triangle.
    1.hypotenuse=?
    shorter leg= ?
    longer leg= 12
    2. hypotenuse=7√3
    shorter leg=?
    longer leg=?
    3. hypotenuse=?
    shorter leg=?
    longer leg=15
    4. hypotenuse=2√2
    shorter leg=?
    longer leg=?
    5. Find the perimeter of a square if a diagonal is 12.
    6. Find the perimeter of an equilateral trianle if an altitude has length 7√3.

    Please explain me about how to solve the square root number like 8√3 x 2√2. and 6 x √3.
    Thank you...^^
    Hope you a lucky day~!!!!!!!!!!
    Last edited by sarayork; November 27th 2007 at 01:46 AM.
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  2. #2
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    Quote Originally Posted by sarayork View Post
    Please solve this following problems.^^*

    Find the sides of the [30-60-90] right triangle.
    1.hypotenuse=?
    shorter leg= ?
    longer leg= 12
    2. hypotenuse=7√3
    shorter leg=?
    longer leg=?
    3. hypotenuse=?
    shorter leg=?
    longer leg=15
    4. hypotenuse=2√2
    shorter leg=?
    longer leg=?
    5. Find the perimeter of a square if a diagonal is 12.
    6. Find the perimeter of an equilateral trianle if an altitude has length 7√3.
    Hello,

    I assume that you are referring to degrees here: "...[30-60-90] right triangle".

    With such a right triangle the ratio of shorter leg to hypotenuse is : \frac{l_s}{h}=\frac12

    Use this formula and the Pythagorean theorem to calculate the missing values:

    to #1: l_s=\frac12 \cdot h Solve the equation

    h^2 = \left(\frac12 \cdot h \right)^2 + 12^2 for h and afterwards calculate the shorter leg.

    The following questions have to be done similarly.

    to #5:

    If the side of the square is a and the diagonal is d you find:

    d^2 = a^2+a^2 = 2a^2 . Use this property to calculate the length of one side and afterwards the perimeter: p = 4 \cdot a

    to #6:

    The altitude of an isosceles triangle with the side a is calculated by: h=\frac12 \cdot a \cdot \sqrt{3}.

    Plug in the known value of h and solve for a. Afterwards calculate the perimeter: p = 3 \cdot a
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