Find Angle with three (x, y) coordinate points

[Alastair]

Really struggling with this, please help!

I need to find the other two (?) lengths to the triangle in the image below. I think I need to work the angle (?) out first then I might be able to find the other two side. I only know three (x,y) coordinates. See image below for context.

Point A
x= 5633
y= -25107.98

Point B
x= 8230.99
y= -23608.03

Point C
x= 6931.72
y= -24357.87


Many thanks in advance!!

 

[tkhunny]

Your post did no time out. Posts do not show up until approved by a moderator. That's all.

You have the coordinates? What is preventing the use of the Distance Formula?

You have the coordinates? Find the equation for Line AB. Use the Normal Form. You'll be done finding Green(?) in a moment. No need for angles or other lengths. Then you can continue.

 

[Deleted member 4993]

Really struggling with this, please help!

I need to find the other two (?) lengths to the triangle in the image below. I think I need to work the angle (?) out first then I might be able to find the other two side. I only know three (x,y) coordinates. See image below for context.

Point A
x= 5633
y= -25107.98

Point B
x= 8230.99
y= -23608.03

Point C
x= 6931.72
y= -24357.87
View attachment 8319

Many thanks in advance!!

As tkhunny suggested

calculate the lengths of BC, CA & AB using L = √[(x₁ - x₂)² + (y₁ - y₂)²]

Then use law of cosines to calculate Cos(CAB) = [ CA² + AB² - BC² ]/[2 * CA * AB]

Be careful about the sign and location of the angles.

 

[Mrspi]

Do a search on Google or your favorite search engine for

formula for perpendicular distance from point to line

You have the coordinates of points A and B; you should be able to find the equation of the line AB. Then apply the formula......and calculate the distance from point C to that line.

I see that Khan Academy has a video lesson on this process....it showed up in MY search for the formula, and it might be helpful!