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A little confused with how to use SOHCAHTOA

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    Hi. Ok, so I know what SOHCAHTOA stands for, and which one you'd use if there was a missing side and angle. For example, you knew the hypotenuse and the adjacent, but you didn't know the opposite, you'd use cos^-1 to find the missing angle.

    However, I don't understand it when you need to work out the length of a side, but know the angle. There's a question that tells you the length of the opposite and the angle, but the hypotenuse value and adjacent value are missing. How do I know which function to use? Please help, thanks.


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    It depends on whether you are trying to find the hypotenuse or the adjacent. The question will tell you which one you need.
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    You can work out one of the missing values using SOHCAHTOA, then use Pythagoras theorem to work out the final side (unless you wanna use SOHCAHTOA for both, which is fine). In your case:

    Sin(x) = y / H where x is the given angle and y is the length of the opposite.

    Re-arrange to get H = y / sin (x) which gives you the hypotenuse length. Repeat for the final length or use Pythagoras.
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    If the opposite is given, the question will then ask you to find one of the lengths, which will be the hypotenuse or the adjacent.

    Eg

    ABC = 90 degrees
    AB = 6

    ACB = 76 degrees.

    Find length BC. (adjacent)

    So you'd use

    Tan76 = 6/BC
    BC = 6/Tan76

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    (Original post by Mr M)
    It depends on whether you are trying to find the hypotenuse or the adjacent. The question will tell you which one you need.
    Ok, so if I needed to find the opposite, I'd use cos?


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    (Original post by Enthusiastic A)
    Ok, so if I needed to find the opposite, I'd use cos?


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    Cos is adjacent/hypotenuse , you'd need sin for that
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    (Original post by Enthusiastic A)
    Ok, so if I needed to find the opposite, I'd use cos?


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    You never use cos for the opposite. cos x is defined as adjacent over hypotenuse.
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    (Original post by joostan)
    Cos is adjacent/hypotenuse , you'd need sin for that
    That's where I'm confused. I don't know the opposite, so how can I use sin (opposite/hypotenuse)? How can I divide the opposite by the hypotenuse when I don't know the value of the oposite?


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    (Original post by Enthusiastic A)
    That's where I'm confused. I don't know the opposite, so how can I use sin (opposite/hypotenuse)? How can I divide the opposite by the hypotenuse when I don't know the value of the oposite?


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    Call the unknown x?
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    (Original post by Enthusiastic A)
    That's where I'm confused. I don't know the opposite, so how can I use sin (opposite/hypotenuse)? How can I divide the opposite by the hypotenuse when I don't know the value of the oposite?


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    How would you solve:

    2 = x/4

    Same thing. Different values.
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    (Original post by Enthusiastic A)
    That's where I'm confused. I don't know the opposite, so how can I use sin (opposite/hypotenuse)? How can I divide the opposite by the hypotenuse when I don't know the value of the oposite?


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    Rotate your page so that the angle you are looking at changes, then you can find that angle using trigonometry. Also as angles in a triangle sum to 180 you can find the required angle.

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