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Math Help - missing angle

  1. #1
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    missing angle

    hi,
    i need to find the missing angle of this triangle marked X:

    missing angle-shape.jpg
    would it be correct to work it out like this:

    cos82= 23/X
    23=Xxcos82
    23/cos82= 165.26
    X=165.26??

    if this is incorrect could you please let me know how i can improve on this to make it correct!

    thanks!
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  2. #2
    Super Member Quacky's Avatar
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    Not quite. Cos(82)=\frac{x}{23}

    Remember 'Sohcahtoa' - Sin = \frac{Opp}{Hyp}; Cos = \frac{Adj}{Hyp}; Tan = \frac{Opp}{Adj}

    Where 'adj' = the line adjacent to the angle, 'opp' = the line opposite the angle, and 'hyp' is the hypotenuse - the longest side.

    I'm sure you can solve from there.

    Edit:I assumed you meant that you wanted to find X. If it's the missing angle you need, then see below.
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  3. #3
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by andyboy179 View Post
    hi,
    i need to find the missing angle of this triangle marked X:

    Click image for larger version. 

Name:	shape.jpg 
Views:	25 
Size:	9.8 KB 
ID:	20997
    would it be correct to work it out like this:

    cos82= 23/X
    23=Xxcos82
    23/cos82= 165.26
    X=165.26??

    if this is incorrect could you please let me know how i can improve on this to make it correct!

    thanks!
    The sum of the interior angles of a triangle is 180 degrees. You have an angle of 82 degrees and a right angle. How do you find the remaining angle?

    -Dan
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  4. #4
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    Oh yes, well spotted quacky I need to find X. Quacky it must be cos because there is nothing opposite the angle 82.
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  5. #5
    Super Member Quacky's Avatar
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    Quote Originally Posted by andyboy179 View Post
    Oh yes, well spotted quacky I need to find X. Quacky it must be cos because there is nothing opposite the angle 82.
    I agree with you there. But according to your diagram, the adjacent angle is the one marked x, and the hypotenuse is 23. Look carefully at my correction.
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  6. #6
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    I'm confused, I know adj is X and hyp is 23
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  7. #7
    Super Member Quacky's Avatar
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    Quote Originally Posted by andyboy179 View Post
    I'm confused, I know adj is X and hyp is 23
    So Cos(82)=\displaystyle\frac{x}{23}, as I said above. You wrote initially: Cos(82)=\displaystyle\frac{23}{x}

    It was just a small mistake, but you get very different answers.
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  8. #8
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    Oh I see and 23 being the biggest side would mean X is smaller than 23. So X = 3.2?
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  9. #9
    Super Member Quacky's Avatar
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    Quote Originally Posted by andyboy179 View Post
    Oh I see and 23 being the biggest side would mean X is smaller than 23. So X = 3.2?
    Yeah, that's right.
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  10. #10
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    Quote Originally Posted by andyboy179 View Post
    23=Xxcos82
    Please use * to indicate multiplication, NOT x ; 23 = X * cos(82)
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