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Math Help - Request for help with 2 triangles problem

  1. #1
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    Request for help with 2 triangles problem

    I have been trying to solve a problem; originally I was thinking of it as 2 circles, but it is basically a problem of triangles, please see the attached file:I know the distance between A and B, the length of r and the angle a. When I draw it out there can only be 1 answer per set of variables, but I can't get a handle on how to calculate any of the other lengths of the triangles' sides.

    If anyone can point me in the right direction I would be greatful.
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  2. #2
    Super Member bigwave's Avatar
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    Quote Originally Posted by EckCop View Post
    I know the distance between A and B, the length of r and the angle a
    can you post what these values are

    but so far looks you use the Law of Sines
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  3. #3
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    values

    Hi bigwave,

    The values are a=5degrees, AB=110, r=66.

    Hope this helps.
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  4. #4
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    Hello, EckCop!

    Solve the triangle.

    Code:
                            C
                            *
                         *      *
                      *             *   66
                   *                    *
                *                           *
             * 5                               *
        A *  *  *  *  *  *  *  *  *  *  *  *  *  *  * B
                            110

    We will find angle C . . . Note: \angle C is obtuse.


    Law of Sines: . \frac{\sin C}{110} \:=\:\frac{\sin 5^o}{66} \quad\Rightarrow\quad \sin C \:=\:0.145259571

    . . \angle C \;=\;8.35231067^o\,\text{ or }\,171.6476893^o

    . . \boxed{\angle C \;\approx\;171.65^o}


    Hence: . \angle B \:=\:180^o - 5^o - 171.65^o \quad\Rightarrow\quad \boxed{\angle B \;\approx\;3.35^o}


    Law of Sines: . \frac{AC}{\sin3.35^o} \:=\:\frac{66}{\sin5^o} \quad\Rightarrow\quad AC \:=\:44.25095312

    . . \boxed{AC \;\approx\;44.25}

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  5. #5
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    Thanks Soroban,

    That is just what I needed.
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