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How to find the X coordinate of a point using trigonometry?

  1. Sep 20, 2013 #1
    How to determine the X coordinate of the red point if i know the Y coordinate and the angle between the adjacent side and the hypotenuse in the formed right triangle(see the image)? I don't know the length of the hypotenuse and the adjacent side of the triangle, i know only the angle between the adjacent side and the hypotenuse and the length of the opposite side(the Y coordinate of the red point). Let's say that Y is 40(i.e. the length of the opposite side) and the angle is 35 degrees. How to determine the X coordinate? Or in other words the length of the adjacent side in the triangle. I asked this on stackoverflow.com but the answer i got wasn't helpful at all. It's very simple question, my native language is not english but i think it's pretty clear what i'm asking.

    http://img27.imageshack.us/img27/4099/ce4n.png [Broken]
     
    Last edited by a moderator: May 6, 2017
  2. jcsd
  3. Sep 20, 2013 #2

    Office_Shredder

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    The main trigonometric functions are sin(x), cos(x) and the one you are going to want to use, tan(x). sin(x) is literally the ratio between the opposite side and hypotenuse of a right triangle with an angle of x in it, cos(x) is the ratio between the adjacent side and hypotenuse of a right triangle with an angle of x in it, and tan(x) is the ratio between the opposite and adjacent sides of a right triangle with an angle of x in it.

    As a side point, it should be clear that tan(x) = sin(x)/cos(x).

    Your example right triangle has an adjacent leg of length X to be determined, the opposite leg has a length of 40, and your angle is 35 degrees. So we have

    tan(35) = 40/X
    X = 40/tan(35).

    You can calculate tan(35) on your calculator (possibly needing the sin(x)/cos(x) thing depending on the type) or by using any of a number of websites. You do have to be careful because there are two ways of measuring angles - radians and degrees - and a lot of places might assume you are inputting your angle in radians. You should try getting tan(35) from a computing source yourself, and the number you should get is very close to .7


    As an exercise to practice, if that point has an X coordinate of 12 and an angle of 50 degrees, what is the length of the hypotenuse?
     
  4. Sep 20, 2013 #3
    So, if the adjacent side is 12 and if by "an angle of 50 degrees" you mean the angle formed by the hypotenuse and the adjacent side(like in my drawing), then cos(50) = 12 / hypotenuse => 0.642 = 12 / hypotenuse => 12 / 0.642 = 18.67

    Thanks. Actually the answer on the website i mentioned was helpful but i didn't paid much attention to it initially. But your answer is more uuh...descriptive and generally better, so thank you again.
     
    Last edited: Sep 20, 2013
  5. Sep 20, 2013 #4

    HallsofIvy

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    You don't mention tangent which is what Office Shredder said was the function you need. tangent is "opposite side over near side" so, in this xy- coordinate system [itex]tan(\theta)= y/x[/tex]. Given that [tex]\theta= 35[/tex] degrees and y= 40, [tex]x= y/tan(\theta)= 40/tan(35)= 40/.7002[/tex].
     
  6. Sep 21, 2013 #5

    Office_Shredder

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    Miro, that looks good to me.

    Halls, he didn't use tan because he was answering the other practice question I gave him
     
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