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Math Help - Easy Trigonometry Problem

  1. #1
    Member Mr Rayon's Avatar
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    Wink Easy Trigonometry Problem

    The angle formed by the diagonal of a rectangle and one of its shorter sides is 60. If the diagonal is 8 cm long, find the dimensions of the rectangle, in surd form.

    I am having trouble imagning this. I am also not sure what the question is asking me to do.

    Any help regarding the problem above will be appreciated!
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  2. #2
    Moo
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    Hello,

    Easy Trigonometry Problem-trigo-rect.jpg

    Just apply the definition of cosine and sine in the right-angled triangle ABC :

    \cos 60=\frac{AC}{BC}

    \sin 60=\frac{AB}{BC}

    and for the values of cos and sin, they're just common values.
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  3. #3
    Member Mr Rayon's Avatar
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    Quote Originally Posted by Moo View Post
    Hello,

    Click image for larger version. 

Name:	trigo rect.JPG 
Views:	42 
Size:	12.3 KB 
ID:	10570

    Just apply the definition of cosine and sine in the right-angled triangle ABC :

    \cos 60=\frac{AC}{BC}

    \sin 60=\frac{AB}{BC}

    and for the values of cos and sin, they're just common values.
    Ok...thanks for the diagram. Now I know what I'm looking at! But I'm afraid I'm still a little lost.
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  4. #4
    Member Mr Rayon's Avatar
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    Smile

    Nevermind...I get it now!

    EDIT:

    See:

    cos 60 = AC/BC
    1/2 = x/8
    8/2= x
    x= 4

    (√3)/2 = AB/BC
    (√3)/2 = x/8
    (8√3)/2 = x
    x= 4√3
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  5. #5
    Moo
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    Quote Originally Posted by Mr Rayon View Post
    Nevermind...I get it now!

    EDIT:

    See:

    cos 60 = AC/BC
    1/2 = x/8
    8/2= x
    x= 4

    (√3)/2 = AB/BC
    (√3)/2 = x/8
    (8√3)/2 = x
    x= 4√3
    Yes
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  6. #6
    Member Mr Rayon's Avatar
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    Quote Originally Posted by Moo View Post
    Hello,

    Click image for larger version. 

Name:	trigo rect.JPG 
Views:	42 
Size:	12.3 KB 
ID:	10570

    Just apply the definition of cosine and sine in the right-angled triangle ABC :

    \cos 60=\frac{AC}{BC}

    \sin 60=\frac{AB}{BC}

    and for the values of cos and sin, they're just common values.
    Hey, moo how'd you draw the right angle triangle? What software/file do you use? How can I do the same thing in a post in this forum?
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  7. #7
    Moo
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    Drew it in paint, then used the attachment option in a post to add it to my post.
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