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Thread: Solve tiangle

  1. #1
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    Solve tiangle

    Solve triangle in which is

    $$ b+c=20,\ a=5\sqrt 2,\ \gamma=135$$

    ($2$ solutions)
    Last edited by ns1954; Jan 15th 2019 at 07:28 AM.
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  2. #2
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    Re: Solve tiangle

    Quote Originally Posted by ns1954 View Post
    Solve triangle in which is
    $$ b+c=20,\ a=5\sqrt 2,\ \gamma=135$$
    ($2$ solutions)
    Normally the word solve is applied to an equation. I don't see any, do you?
    So you need to explain and show some effort. This is not a homework service.
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  3. #3
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    Re: Solve tiangle

    u = alpha, v = beta, w = gamma
    w = 135, v = 180 - 135 - u = 45 - u

    5sqrt(2) / SIN(u) = (20-b) / SIN(135) = b / SIN(45 - u)

    Above is a hint.
    Sorry, homework not done here...

    Not sure what you're solving for...so solve for whatever turns you on!!
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  4. #4
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    Re: Solve tiangle

    Solve triangle means find basic elements of triangle
    $$ a,\ b,\ c,\ \alpha,\ \beta,\ \gamma.$$
    I have solutions which demand picture which I don't know how to draw. And, please somebody to tell me where to post problems like challenges.

    If $D-C-A,\ and\ BD=h_b$ then $BD=DC=5$ and from $\Delta ABD$ with Pithagoras law we have

    $$(20-b)^2=5^2+(b+5)^2$$

    which gives $b=7$. Te rest is easy, but this give me just one solution.
    Last edited by ns1954; Jan 15th 2019 at 10:41 AM.
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  5. #5
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    Re: Solve tiangle

    Quote Originally Posted by ns1954 View Post
    Solve triangle means find basic elements of triangle
    $$ a,\ b,\ c,\ \alpha,\ \beta,\ \gamma.$$
    I have solutions which demand picture which I don't know how to draw. And, please somebody to tell me where to post problems like challenges.

    If $D-C-A,\ and\ BD=h_b$ then $BD=DC=5$ and from $\Delta ABD$ with Pithagoras law we have

    $$(20-b)^2=5^2+(b+5)^2$$

    which gives $b=7$. Te rest is easy, but this give me just one solution.
    No idea what you're doing...
    You gave one of the angles as 135: so IMPOSSIBLE for triangle to be a right triangle...

    Are you a student attending math classes?
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  6. #6
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    Re: Solve tiangle

    Ha, ha, ha, I'm professor of math from Serbia. Draw the picture, all is clear.
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    Re: Solve tiangle

    Quote Originally Posted by ns1954 View Post
    If $D-C-A,\ and\ BD=h_b$
    What the hell does that mean????

    Can you at least describe what the diagram would look like?
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  8. #8
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    Re: Solve tiangle

    Quote Originally Posted by DenisB View Post
    What the hell does that mean????
    Can you at least describe what the diagram would look like?
    Denis, $D-C-A$ is standard notation is axiomatic geometry. It means that $D,~C,~\&~A$ are colinear points and $C$ is between $D~\&~A$.
    But I'll be damn if I know what this professor troll means by it.
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  9. #9
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    Re: Solve tiangle

    It's always interesting when the first problem is trying to decipher what the poster is really trying to do. I have attached picture below (not necessarily to scale) of my best guess of what the professor is looking for. I'm guessing the $135^\circ$ may be interior or exterior to the triangle giving an alternate angle $A'$ and corresponding adjacent sides $b'$ and $c'$ to give two triangles.
    Here's a picture (click on it to expand):
    Attached Thumbnails Attached Thumbnails Solve tiangle-figure.jpg  
    Last edited by Walagaster; Jan 15th 2019 at 06:43 PM.
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    Re: Solve tiangle

    Only someone from Tempe AZ could figure that out

    Also looks like a 7-24-25 right triangle is involved...right?
    Last edited by DenisB; Jan 15th 2019 at 07:07 PM.
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    Re: Solve tiangle

    Quote Originally Posted by ns1954 View Post
    Ha, ha, ha, I'm professor of math from Serbia. Draw the picture, all is clear.
    Quote Originally Posted by Walagaster View Post
    It's always interesting when the first problem is trying to decipher what the poster is really trying to do. I have attached picture below (not necessarily to scale) of my best guess of what the professor is looking for. I'm guessing the $135^\circ$ may be interior or exterior to the triangle giving an alternate angle $A'$ and corresponding adjacent sides $b'$ and $c'$ to give two triangles.
    Here's a picture (click on it to expand):
    Solve tiangle-figure.jpg

    @ns1954: Is Walagaster's diagram the one you are using? I don't think we can help you out if we don't have anything more to work with.

    -Dan
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  12. #12
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    Re: Solve tiangle

    Walagaster's draw is Ok, same I used, without point A'. $h_b$ is altitude of triangle, and $\Delta BDC$ is isosceles, right triangle. My native language is serbian, and we use specific termilology for elements of triangle for which I'm not sure I know the english terms. I find this problem in book of probems, and author claims that exist 2 solutions. I see only one.
    $\alpha=\arcsin\frac {5}{13}$ and $\beta=\frac {7}{13\sqrt 2}$.
    Last edited by ns1954; Jan 15th 2019 at 10:01 PM.
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  13. #13
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    Re: Solve tiangle

    @DenisB
    Your hint leeds also to $b=7$, but with draw it gets easier and faster.
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  14. #14
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    Re: Solve tiangle

    Quote Originally Posted by ns1954 View Post
    @DenisB
    Your hint leeds also to $b=7$, but with draw it gets easier and faster.
    I'll never attend your math classes

    B


    5


    D.......5........C........7..............A

    BA = 13
    Triangle BCD is isosceles...so angle BCA = 135

    WHY do you not use Walagaster's point A' ?
    Seems to be only way for YOUR 2nd solution.
    I pity your poor students
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  15. #15
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    Re: Solve tiangle

    $\gamma=135$ is given interior angle of triangle, so A' is of no use.
    BTW, I'm in retirement, and I was not happy with the students. I feel like a sigh whose song nobody heard. Some like you.
    Last edited by ns1954; Jan 16th 2019 at 08:28 AM.
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