Results 1 to 4 of 4

Math Help - Special Right Triangles

  1. #1
    Member
    Joined
    Aug 2007
    Posts
    183

    Special Right Triangles

    Could someone please check my work? I was assigned multiples of 3...so there arent very many..I also skipped a few that I did not understand...
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    9,927
    Thanks
    332
    Awards
    1
    Quote Originally Posted by aikenfan View Post
    Could someone please check my work? I was assigned multiples of 3...so there arent very many..I also skipped a few that I did not understand...
    In all of your problems you are dealing with a specific kind of right triangle: one where the two legs are equal. So
    x^2 + y^2 = z^2

    x^2 + x^2 = z^2 <-- Since y = x

    2x^2 = z^2

    If you are given one of the legs, you know the other one is equal to the given leg. If you are looking then for z then solve the above equation for z.

    If you are given z then you know the two legs are equal and equal to x in the above equation. So solve it for x.

    Example: You are given y = 5. Thus x = y = 5. And
    z = \sqrt{2} \cdot x = \sqrt{2} \cdot 5 = 5 \sqrt{2}.

    Example: You are given z = 20. Thus x = \frac{z}{\sqrt{2}} = \frac{20}{\sqrt{2}}
    (Which simplifies to 10 \sqrt{2}.)

    Doing the other kinds of triangles involves a similar process, though, of course, x and y may not be equal. Either way we still have x^2 + y^2 = z^2 and you can work from there.

    -Dan
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,735
    Thanks
    642
    Hello, aikenfan!

    You did quite good . . . the ones you skipped are rather tricky.


    For 1 - 10:
    Code:
                        *
                      * *
                    *45*
               z  *     *
                *       * y
              *         * 
            * 45       *
          * * * * * * * *
                 x

    \begin{array}{ccccc} & x & y & z \\ \\<br />
3) & {\color{blue}10} & 10 & {\color{blue}10\sqrt{2}} & \text{Correct!} \\ \\<br /> <br />
6) & {\color{blue}6\sqrt{2}} & {\color{blue}6\sqrt{2}} & 12 & \text{Right!} \\ \\<br /> <br />
9) & {\color{blue}-} & {\color{blue}-} & 5\sqrt{10} & \end{array}


    For the 45-45-90 triangle, think of the sides as: . \begin{array}{ccc}x & = &a \\ y & = & a \\ z & = & a\sqrt{2}\end{array}
    So, if we know one side, we can find the others.



    In #3, we are given: y \,= \,10

    Then: . x \,= \,10,\;z \,= \,10\sqrt{2}



    In #6, we are given: z \,=\,a\sqrt{2} \,=\,12

    Divide both sides by \sqrt{2}\!:\;\;\frac{a\sqrt{2}}{\sqrt{2}}\:=\:\fra  c{12}{\sqrt{2}}\quad\Rightarrow\quad a \:=\:\frac{12}{\sqrt{2}}

    Rationalize: . a \:=\:\frac{12}{\sqrt{2}}\cdot\frac{\sqrt{2}}{\sqrt  {2}} \:=\:\frac{12\sqrt{2}}{2} \:=\:6\sqrt{2}

    Therefore: . x \,=\,y\,=\,6\sqrt{2}



    In #9, we are given: . z \,=\,a\sqrt{2}\,=\,5\sqrt{10}

    Divide both sides by \sqrt{2}\!:\;\;\frac{a\sqrt{2}}{\sqrt{2}}\:=\:\fra  c{5\sqrt{10}}{\sqrt{2}} \quad\Rightarrow\quad a \:=\:5\sqrt{5}


    . . \begin{array}{cccc}9)\; & \;{\color{blue}5\sqrt{5}}\; & \;{\color{blue}5\sqrt{5}}\; & \;5\sqrt{10} \end{array}


    ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

    Try the same technique on the other problems.

    For the 30-60-90 triangle, think of them as: . \begin{array}{ccc}x & = & a\sqrt{3} \\ y & = & a \\ z & = & 2a\end{array}
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member
    Joined
    Aug 2007
    Posts
    183
    I think that I have got it now, I am going to repost my work that I have changed to make sure that I am on the right track....
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Special right triangles
    Posted in the Geometry Forum
    Replies: 1
    Last Post: January 7th 2010, 03:50 PM
  2. Help With Special Right Triangles
    Posted in the Geometry Forum
    Replies: 1
    Last Post: October 31st 2008, 12:12 PM
  3. Special Right Triangles
    Posted in the Trigonometry Forum
    Replies: 4
    Last Post: October 30th 2007, 02:07 PM
  4. Special Triangles
    Posted in the Geometry Forum
    Replies: 3
    Last Post: May 6th 2007, 01:30 PM
  5. Help with a special right triangles problem
    Posted in the Geometry Forum
    Replies: 1
    Last Post: April 22nd 2007, 11:47 AM

Search Tags


/mathhelpforum @mathhelpforum