How to solve a triangle formed by three (x,y) points.
Plot three points on the (x,y) plane and join them with lines. If the points are not in the same straight line, you will have created a triangle. This diagram shows the triangle created by the three points (1,3), (-2,-2) and (3,-1):
This triangle has internal angles 'A', 'B' and 'C', and sides of length 'a', 'b' and 'c':
The distance formula can be used to find the distance between two (x,y) points.
For example, consider the points (x1, y1) and (x2, y2). The distance 'd' between them is given by the formula:
We can use the distance formula to find the distance between each pair of points making up our triangle. These distances are the lengths of the three sides.
For the example above, the points are: (1,3), (-2,-2) and (3,-1), so we calculate the side lengths by taking these points two at a time:
Side 1 joining (1,3) and (-2,-2)
Similarly, the side joining (1,3) and (3,-1) is 4.47214, and
the side joining (-2,-2) and (3,-1)is 5.09902
We now know the three side lengths of the triangle, as shown below:
Once the three side measurements are known, then the internal angles 'A', 'B' and 'C' can be found as well.
When no angles are known, the cosine rule is the only option.
Step 1: Begin by using the cosine rule to find the largest angle.
The largest angle is always opposite to the largest side, so this is angle 'B' in this example ...
Step 2: Use the sine rule to find one of the remaining angles.
Step 3: Use the 'sum of internal angles' rule to find the third angle...
The triangle is now solved. This diagram shows all of the sides and angles:
Maths Helper Plus can solve a triangle given three (x,y) points. Full working steps and a labelled diagram are created. The steps below will show you how...
Step 2 Display the triangle solver options box
Double click the mouse in the border to the left of the calculations. ( This area is shaded pale blue in the diagram below.) The triangle solver options box will display its '3 Points' tab...
Click the 'Clear' button to remove the previous triangle, then click on the edit box near angle 'A' (lower left). Type the (x,y) point for the lower left point of your triangle. Repeat for the other two points.
Click the 'OK' button to close the options box. The calculations and triangle diagram will be displayed on your screen.
Step 3 Adjust the size of the diagram
If the triangle diagram is too big to display properly on your computer screen, briefly press the F10 key to reduce its size. To make the diagram bigger, hold down a Ctrl key while you press F10.