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Math Help - solve the triangle/with given parts

  1. #1
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    solve the triangle/with given parts

    alpha=42.5degree
    beta=35.2degree
    a=18.0
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  2. #2
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    Quote Originally Posted by colie2020 View Post
    alpha=42.5degree
    beta=35.2degree
    a=18.0
    \alpha + \beta + \gamma = 180^\circ

    find \gamma , then use the sine law.
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  3. #3
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    Quote Originally Posted by colie2020 View Post
    alpha=42.5degree
    beta=35.2degree
    a=18.0
    I'm assuming side A is directly opposite angle \alpha, there is a side B opposite angle \beta, and there is a hypotenuse opposite angle \gamma.

    If so...

    The sum of the interior angles in a triangle equals 180, so:
    <br />
\alpha + \beta + \gamma = 180<br />

    <br />
42.5 + 35.2 + \gamma = 180<br />

    <br />
\gamma = 102.3<br />

    The Law of Sines:



    <br />
\frac{18}{\sin (42.5)} = \frac{B}{\sin (35.2)}<br />

    <br />
B = \frac{18\sin (35.2)}{\sin (42.5)}<br />

    <br />
\frac{18}{\sin (42.5)} = \frac{C}{\sin (102.3)}<br />

    <br />
C = \frac{18\sin (102.3)}{\sin (42.5)}<br />

    Check out the wikipedia entry on the law of sines:
    Law of sines - Wikipedia, the free encyclopedia

    What this problem is asking is known as triangulation:
    Triangulation - Wikipedia, the free encyclopedia
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