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Math Help - Soh Cah Toa help

  1. #1
    Junior Member mattballer082's Avatar
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    Soh Cah Toa help

    in geometry, is anyone familiar with SOH CAH TOA?

    First, what is the definition of adjacent and how do i know which angle is adjacent and which angle is opposite. I know which is the hypotenuse.
    How would I use it with SINE COSINE and TANGENT??

    Very confused here please help.
    Last edited by MathGuru; July 6th 2005 at 05:23 PM.
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  2. #2
    Site Founder Math Help's Avatar
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    Lightbulb Opposite and adjacent

    In short, opposite is the side opposite any angle you are taking the sin, cos or tan of. Adjacent is the side that is part of(or next to) the angle but not the hypotenuse.

    Remember that Soh Cah Toa always refers to right triangles (triangles with at least one 90 degree angle).

    The hypotenuse is always the side opposite the 90 degree angle.

    in fact the hypotenuse is the opposite for the 90 degree angle, take a look:

    sin=\frac{opposite}{hypotenuse}

    sin(90)=1

    1=\frac{opposite}{hypotenuse}

    therefore

    opposite=hypotenuse

    And that is why sin(90) = 1, because the hypotenuse is opposite the right angle.

    I hope I didn't confuse you too much.
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  3. #3
    MHF Contributor
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    I am not familiar with SOH CAH TOA (they were not taught to us in school back then), but I have encountered those more than once, so I can explain them.

    SOH
    S = O/H
    Sine = Opposite / Hypotenuse


    CAH
    C = A/H
    Cosine = Adjacent / Hypotenuse

    TOA
    T = O/A
    Tangent = Opposite / Adjacent

    SOH CAH TOA then is a way to memorize or recall which one, or what is sine, cosine or tangent.

    Of course you know that sine, cosine and tangent are trigonometric functions of an angle.
    This angle is imagined as one of the two acute angles of a right triangle.

    A right triangle has a hypotenuse, which is the longest of the 3 sides, and two other sides that are perpendicular to each other. These other two perpendicular sides are sometimes called "legs" of the right triangle.

    The angle in question is opposite to one of these two legs. The angle then is adjacent to the other leg.
    The leg opposite to the angle is the "Opposite"
    The leg adjacent to the angle is the "Adjacent"
    The hypotenuse is always the "Hypotenuse" :-)
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  4. #4
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    Just to emphasise: adjacent means next to, neighbouring, bordering on, beside.
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