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Trigonometry find the opposite side

  1. May 10, 2012 #1
    I'm a bit curious on how do I find the length of the Opposite side of a Right Triangle,
    now I have look a Soh Cah Toa, Now say if I know the length of the Adjacent Line and the the angle of the right triangle which formula should I use?

    I thought about Toa is this the way I solve for the opposite?

    opposite = tan degree / adjacent
  2. jcsd
  3. May 10, 2012 #2


    Staff: Mentor

    Do you understand what the mnemonic SOH-CAH-TOA means?

    In response to your question, it's NOT true that "opposite = tan degree / adjacent". The correct formula is tan(##\theta##) = oppposite/adjacent, where ##\theta## is the acute angle you're looking at, opposite is the side opposite to ##\theta##, and adjacent is the side that is between ##\theta## and the right angle.
  4. May 10, 2012 #3
    Yes I understand Soh Cah Toa but I am using the equation to find the side of an unknown
    side and the formula I'm using is

    tan = opposite / adjacent
    but I only have the opposite side and the angle so to find the adjacent side I used this formula

    24 / tan 42 degrees = 26.654700355900628883443567139963

    adjacent side = 26.654700355900628883443567139963

    But now the side I want to find is the Opposite side, do I used the same equation but put the angle tan degree in the Opposite side and divide by the adjacent side to find the Opposite side

    tan degree / adjacent = Opposite side ?

    opposite = ?
  5. May 10, 2012 #4
    Sorry my mistake The formula I should of used is

    adjacent * tan = opposite


    12 * tan24 = 5.342744223702433967068404367748
  6. May 10, 2012 #5


    Staff: Mentor

    It's pretty simple algebra. The basic formula is
    tan(θ) = O/A ...... (1)

    If you know the angle, θ, and the adjacent side A, and you want to find the opposite side O, multiply both sides of the equation above by A.
    This gives you O = A*tan(θ)

    If you know the angle and the opposite side O, and you want the adjacent side, A, multiply both sides of equation 1 by A, and then divide both sides by tan(θ).

    tan(θ) = O/A
    A*tan(θ) = O
    A = O/tan(θ)
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