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

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Discussion Overview

The discussion centers around determining the X coordinate of a point in a right triangle using trigonometric functions, specifically when the Y coordinate and the angle between the adjacent side and the hypotenuse are known. Participants explore the application of trigonometric ratios to solve for the unknown side length.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Homework-related

Main Points Raised

  • One participant asks how to find the X coordinate given the Y coordinate (40) and the angle (35 degrees) without knowing the lengths of the hypotenuse or adjacent side.
  • Another participant explains the use of trigonometric functions, particularly tangent, to relate the sides of the triangle, stating that tan(35) = 40/X leads to X = 40/tan(35).
  • A different participant provides a practice problem involving a different angle (50 degrees) and an adjacent side length (12), calculating the hypotenuse using cosine.
  • One participant emphasizes the importance of tangent in the context of the original question, reiterating the relationship tan(θ) = y/x.
  • Another participant acknowledges the helpfulness of the previous answers while expressing a preference for the clarity of the explanations provided in the thread.

Areas of Agreement / Disagreement

Participants generally agree on the use of trigonometric functions to solve the problem, particularly the relevance of tangent. However, there is no consensus on the best approach or the clarity of previous answers, as some participants express differing levels of understanding and appreciation for the explanations given.

Contextual Notes

Some participants note the potential confusion regarding angle measurement (degrees vs. radians) and the importance of correctly applying trigonometric functions based on the triangle's configuration.

Who May Find This Useful

This discussion may be useful for students or individuals seeking to understand the application of trigonometry in solving problems related to right triangles, particularly in determining unknown side lengths based on given angles and other side lengths.

Miroslava89
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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
 
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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 .7As 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?
 
Office_Shredder said:
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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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 tan(\theta)= y/x[/tex]. Given that \theta= 35 degrees and y= 40, x= y/tan(\theta)= 40/tan(35)= 40/.7002.
 
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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