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Math Help - Help me find the angle

  1. #1
    ADY
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    Help me find the angle

    So we have a R-H triangle, the hypotenuse is 5cm and the 1 of the angles measures  \frac {1}{8} \pi

    heres how i found the 3rd angle (x), in radians:
    <br />
\frac{1}{8} \pi  = 22.5

    so angle is 90- 22.5 = 67.5

    sin22.5 = \frac {5}{x} , so x = \frac {5}{sin22.5} = 13.06 or .228 radians

    Is this right, and how could i find the answer to my question without converting to degrees?

    More over how could i find the length of the other two sides?

    Thanks
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  2. #2
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by ADY View Post
    So we have a R-H triangle, the hypotenuse is 5cm and the 1 of the angles measures  \frac {1}{8} \pi

    heres how i found the 3rd angle (x), in radians:
    <br />
\frac{1}{8} \pi = 22.5

    so angle is 90- 22.5 = 67.5

    sin22.5 = \frac {5}{x} , so x = \frac {5}{sin22.5} = 13.06 or .228 radians

    Is this right, and how could i find the answer to my question without converting to degrees?

    More over how could i find the length of the other two sides?

    Thanks
    Yeah, degrees never should have came into the picture.

    Angle three is given by

    \overbrace{\frac{\pi}{2}}^{90^\circ}-\frac{\pi}{8}=\frac{4\pi}{8}-\frac{\pi}{8}=\frac{3\pi}{8}

    Understand?
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  3. #3
    Senior Member nikhil's Avatar
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    Lightbulb correction

    sin(22.5)=x/5
    so x=5sin(22.5) and similarly other side will be
    y=5cos(22.5)
    if 0ne angle is pi/8 other will be (pi/2)-(pi/8)=3pi/8
    you may calculate sin(3pi/8) if you don't want degree system.
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  4. #4
    ADY
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    Quote Originally Posted by VonNemo19 View Post
    Yeah, degrees never should have came into the picture.

    Angle three is given by

    \overbrace{\frac{\pi}{2}}^{90^\circ}-\frac{\pi}{8}=\frac{4\pi}{8}-\frac{\pi}{8}=\frac{3\pi}{8}

    Understand?
    Not really - so your saying

     \frac{3\pi}{8}

    is the size of the third angle?
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  5. #5
    MHF Contributor
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    Quote Originally Posted by ADY View Post
    Not really - so your saying

     \frac{3\pi}{8}

    is the size of the third angle?

    it is .
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  6. #6
    ADY
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    So how do i find the lengths of the other two sides?
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  7. #7
    MHF Contributor
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    Quote Originally Posted by ADY View Post
    So how do i find the lengths of the other two sides?

    By doing some trigo .

    \sin \frac{\pi}{8}=\frac{x}{5}

    Then use the phythagoras theorem to get the other side .
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  8. #8
    ADY
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    Im seriously at a loss with this, thank you for your help up to now, but can you talk me through it
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  9. #9
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    \pi radians is equal to 180 degrees

    your calculator can most probably calculate sine of this using degrees or radians.

    one angle is \frac{\pi}{8}

    sin(\frac{\pi}{8})=\frac{opposite}{hypotenuse}=\fr  ac{x}{5}

    x=5sin(\frac{\pi}{8})=1.9134cm

    There are two ways to find the other side;
    cos(\frac{\pi}{8})=\frac{adjacent}{hypotenuse}=\fr  ac{y}{5}

    and y=5cos(\frac{\pi}{8})=5(0.9239)=4.61939cm

    or you could use pythagoras' theorem.

    y^2+(1.9134)^2=5^2
    y^2=21.339
    y=4.16194cm

    to find the other angle working in radians

    \frac{\pi}{2}=\frac{180}{2}=90degrees
    so
    \frac{\pi}{2}-\frac{\pi}{8}=\frac{3\pi}{8}radians

    \frac{3\pi}{8}=\frac{3(180)}{8}=67.5degrees

    which is what you got as your other angle.

    did i leave anything out?
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  10. #10
    ADY
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    so the other two lengths are:

    1.9134cm & 4.61939cm ?
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  11. #11
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    yes
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