# Triangle values by coordinates of vertices

This online calculator calculates a set of triangle values: length of sides, angles, perimeter, and area by coordinates of its vertices

This online calculator is designed to quickly calculate a number of characteristics of a triangle by the coordinates of its vertices. You enter the coordinates of the vertices A, B, and C. The calculator calculates the following values ​​from the coordinates:

• the length of the side a - the side opposite to the vertex A
• the length of the side b - the side opposite to vertex B
• the length of the side c - the side opposite to vertex C
• the value of the angle α at the vertex A
• the value of the angle β at the vertex B
• the value of the angle γ at the vertex C
• the perimeter of the triangle
• area of ​​a triangle

If you need something else, write in the comments, we'll add it. The formulas for calculating triangle values ​​are described under the calculator.

#### Vertex C

Digits after the decimal point: 2
Side a

Side b

Side c

Angle α

Angle β

Angle γ

Perimeter

Area

### Calculating a triangle by the coordinates of the vertices

The lengths of the sides are found by the formula for calculating the distance between points in Cartesian coordinates
$c = l_ {AB} = \ sqrt {(x_2-x_1) ^ 2 + (y_2-y_1) ^ 2}$

The angles are from the formulas for the dot product of vectors at the vertices.
$\mathbf {a} \cdot \mathbf {b} =\|\mathbf {a} \|\ \|\mathbf {b} \|\cos \gamma$

The perimeter is found by simply adding the lengths of the sides.
$P = a + b + c$

The area of ​​a triangle is found through the determinant
$S=\pm \frac{1}{2} \left| \begin{matrix} x_1 - x_3 & y_1 - y_3 \\ x_2 - x_3 & y_2 - y_3 \end{matrix} \right|=\pm \frac{1}{2} \left( (x_1 - x_3)(y_2 - y_3) - (y_1 - y_3)(x_2 - x_3) \right)$

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