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Thread: Soh Cah Toa help

  1. #1
    Junior Member mattballer082's Avatar
    Mar 2005
    Los angeles

    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; Jul 6th 2005 at 04:23 PM.
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  2. #2
    Site Founder Math Help's Avatar
    Apr 2005

    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:

    $\displaystyle sin=\frac{opposite}{hypotenuse}$

    $\displaystyle sin(90)=1$

    $\displaystyle 1=\frac{opposite}{hypotenuse}$


    $\displaystyle opposite=hypotenuse$

    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
    Apr 2005
    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.

    S = O/H
    Sine = Opposite / Hypotenuse

    C = A/H
    Cosine = Adjacent / Hypotenuse

    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
    Senior Member
    Jun 2005
    Just to emphasise: adjacent means next to, neighbouring, bordering on, beside.
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