Mathematical steps to work out top coordinates of a triangle when given bottom coordinates and angles.

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jackfrost

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So I'm trying to write code to figure this problem out, and I can't figure out the mathematical steps to find it out.

I want to know how to find the top coordinates of a triangle when given the bottom two's angles, and the bottom two's coordinates.
triangle problem.png
If this can only be done when one side of the triangle is a right angle then that is fine also.

Many thanks!
 
jackfrost said:
So I'm trying to write code to figure this problem out, and I can't figure out the mathematical steps to find it out.

I want to know how to find the top coordinates of a triangle when given the bottom two's angles, and the bottom two's coordinates.
triangle problem.png
If this can only be done when one side of the triangle is a right angle then that is fine also.

Many thanks!
Click to expand...
We want to see what ideas you have, as well as how much trigonometry you know, in order to help you use what you have learned as much as possible (so we don't have to do all the work for you -- and because if you're going to be doing graphical programming, you'll need to learn these things). There are many ways you could approach this.

Here's an accurate picture of your problem:

1641736833546.png​

Here's a distorted version (different angles) to make it easier to talk about:

1641737094827.png​

My own thought is to write equations for the lines AC and BC, using the slope of AB to find angle [imath]\theta[/imath], and adding [imath]\alpha[/imath] to find the slope of AC, and similarly for BC. Since BC is perpendicular in your example, you might start with that, to show us what you know.

You can use that idea, or one of your own, to get started.
 
Dr.Peterson said:
We want to see what ideas you have, as well as how much trigonometry you know, in order to help you use what you have learned as much as possible (so we don't have to do all the work for you -- and because if you're going to be doing graphical programming, you'll need to learn these things). There are many ways you could approach this.

Here's an accurate picture of your problem:


Here's a distorted version (different angles) to make it easier to talk about:


My own thought is to write equations for the lines AC and BC, using the slope of AB to find angle [imath]\theta[/imath], and adding [imath]\alpha[/imath] to find the slope of AC, and similarly for BC. Since BC is perpendicular in your example, you might start with that, to show us what you know.

You can use that idea, or one of your own, to get started.
Click to expand...
1641739676424.png
The numbers don't really matter as it's the theory of how it's done that I'm after.

I think from there I need to add on the distance from the side (1666.12) from the first angle (on the image it would be the bottom left one) as that won't always be going down a flat plane.
1641740862507.png

Using this example I think my question is how do you figure out the top coords knowing 6.218 up at an angle of 104° from (5,0).

I apologise for my dreadful wording.
 
jackfrost said:
View attachment 30563
The numbers don't really matter as it's the theory of how it's done that I'm after.

I think from there I need to add on the distance from the side (1666.12) from the first angle (on the image it would be the bottom left one) as that won't always be going down a flat plane.
View attachment 30564

Using this example I think my question is how do you figure out the top coords knowing 6.218 up at an angle of 104° from (5,0).

I apologise for my dreadful wording.
Click to expand...
Thanks for showing that you can do at least right-angle trigonometry well, and have a good start on the problem.

You didn't say how you found that 104°, but it's right, and implies you know how to find the angle I called [imath]\theta[/imath]. Good.

To continue this method, you have a starting point B, a direction (104°), and a distance (6.218). So if you drop a vertical line from C, you will have a right triangle with known angle and hypotenuse. What trig functions will tell you the legs of that triangle, from which you can find the desired coordinates? You're very close.

To extend this method to non-right triangles, you can use the Law of Sines to find BC rather than just using the tangent, and do the rest of the work the same way.
 
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