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Math Help - Find Hypotenuse when given two angles and side

  1. #1
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    Find Hypotenuse when given two angles and side

    Hello. I was hoping someone would be able to help with this problem I have.

    I have a right triangle. I need to find the hypotenuse x.

    I am given the opposite side of 20 and the θ of 32 degrees. How do I find the hypotenuse with all this?

    If you would be able to explain how you got the answer, I would really appreciate it. I know this work isn't going anywhere anytime soon so I would really like to learn how to do this for future reference. Thank you so much guys.
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  2. #2
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    Re: Find Hypotenuse when given two angles and side

    Hello, DreadfulGlory!

    In a right triangle, an acute angle is 32^o and the opposite side has length 20.
    Find the length of the hypotenuse.

    Code:
          *
          *   *
      opp *       *    hyp
       20 *           * x
          *               *
          *             32o   *
          *  *  *  *  *  *  *  *  *
                     adj
    We know that: . \sin\theta \:=\:\frac{opp}{hyp}

    So we have: . \sin32^o \:=\:\frac{20}{x}

    Hence: . x \;=\;\frac{20}{\sin32^o} \;=\;37.7415983

    Therefore: . x \;\approx\;37.7
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  3. #3
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    Re: Find Hypotenuse when given two angles and side

    Thank you so much. Great answer.
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