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

## Main Question or Discussion Point

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]

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Office_Shredder
Staff Emeritus
Gold Member
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?

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?
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.

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HallsofIvy
Homework Helper
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 $$\theta= 35$$ degrees and y= 40, $$x= y/tan(\theta)= 40/tan(35)= 40/.7002$$.

Office_Shredder
Staff Emeritus