# Triangle Calculator to SolveSSS, SAS, SSA, ASA, and AAS Triangles

The Triangle Calculator on this page will solve triangles given any one of five combinations of three known measurements, and show its work!

This free online triangle solver will take three known triangle measurements and solve for the other three.

The calculator will also solve for the area of the triangle, the perimeter, the semi-perimeter, the radius of the circumcircle and the inscribed circle, the medians, and the heights.

Plus, unlike other online triangle calculators, this calculator will show its work by detailing each of the steps it took to solve the formulas for finding the missing values.

Finally, the triangle calculator will also calculate the coordinates of the vertices, the centroid, and the circumcenter, and draw the solved triangle based on those coordinates (requires latest version of your web browser software).

With that, let's use the Triangle Calculator to find the three unknown values from the three known values.

Triangle Calculator

Instructions: Select your rounding preference and indicate whether you will be entering angles in "degrees" or "radians".

Next, select either SSS, SAS, SSA, ASA, or AAS to indicate the triangle's known values.

Next, enter the three known values.

Finally, tap or click the "Solve" button. This will solve for the missing sides and/or angles, show the steps taken to solve the triangle, and, if you have an HTML5 compatible web browser, draw the triangle.

Mouse over the blue question marks for a further explanation of each entry field or button. More in-depth explanations and formulas can be found in the glossary of terms located beneath the Triangle Calculator.

IMPORTANT: Please double-check my calculations before considering them to be valid, as I can't test for all possible entries. If you do discover an issue with the calculations, please contact me and let me know the settings and entries that generated the issue so I can trouble-shoot the problem. Thank you!

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Number of decimal places to round result to:
Angles stated in:
Known Values:
SSS - 3 side lengths
SAS - 2 sides and the included angle given
SSA - 2 sides and non-included angle given
ASA - a side and 2 adjacent angles
AAS - a side, 1 adjacent angle, and the opposite angle
SSS: Enter the 3 Sides
Side a length:
Side b length:
Side c length:
Triangle Solution
Triangle classification:
Side a:
Side b:
Side c:
Angle A:
Angle B:
Angle C:
Perimeter:
Semi-Perimeter:
Area:
Median ma:
Median mb:
Median mc:
Height ha:
Height hb:
Height hc:
Vertex A coordinate:
Vertex B coordinate:
Vertex C coordinate:
Centroid coordinate:
Circumcenter coordinate:
I will show my work here.
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### Triangle Calculator Glossary of Terms

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Number of decimal places to round result to: Select how many decimal places you would like the result rounded to. Note that you can change the number of places before or after solving the triangle.

Angles stated in: Select whether you will be entering angle values as degrees or radians

Known Values: Select the radio button that indicates which three of the triangle values are known. Upon making your selection the triangle calculator will load the appropriate entry form.

SSS triangle: Select this option if three sides lengths are known.

SAS triangle: Select this option if two sides lengths and their included angle are known.

SSA triangle: Select this option if two sides lengths and one of their non-included angles are known. This option may yield 0, 1, or 2 solutions.

ASA triangle: Select this option if a side and its two adjacent angles are known.

AAS triangle: Select this option if a side, an adjacent angle, and the side's opposite angle are are known.

Triangle classification: This is the type of triangle (equilateral, isosceles, or scalene, and right, acute, or obtuse) based on the entered and computed triangle values.

Side a: This is the length of side a of the solved triangle.

Side b: This is the length of side b of the solved triangle.

Side c: This is the length of side c of the solved triangle.

Angle A: This is the angle of vertex A of the solved triangle, expressed as either degrees or radians, depending on your selected preference.

Angle B: This is the angle of vertex B of the solved triangle, expressed as either degrees or radians, depending on your selected preference.

Angle C: This is the angle of vertex C of the solved triangle, expressed as either degrees or radians, depending on your selected preference.

Perimeter: This is the perimeter (P) of the solved triangle. The formula used is P = a + b + c.

Semi-Perimeter: This is the semi-perimeter (s) of the solved triangle. The formula used is s = (a + b + c) / 2.

Area: This is the area (K) of the solved triangle. The formula used is K = (base x height) / 2.

Radius of inscribed circle: This is the radius (r) of the inscribed circle of the solved triangle. The inscribed circle is the largest circle that will fit within the triangle. The formula used to find the radius is, r = sqrt[ ((s-a)(s-b)(s-c)) / s], where s is the semi-perimeter of the triangle.

Radius of circumscribed circle: This is the radius (R) of the circumscribed circle of the solved triangle. The circumscribed circle is a circle that passes through all three vertices of a triangle. The formula used to find the radius is, R = (abc) / (4K), where K is the area of the triangle.

Median ma: This is the length of the median (ma), which is the line that runs from vertex A to the mid-point of side a (the opposite side). The formula used for finding the length of the line is, ma = (1/2)sqrt[2c2 + 2b2 - a2].

Median mb: This is the length of the median (mb), which is the line that runs from vertex B to the mid-point of side b (the opposite side). The formula used for finding the length of the line is, mb = (1/2)sqrt[2c2 + 2a2 - b2].

Median mc: This is the length of the median (mc), which is the line that runs from vertex C to the mid-point of side c (the opposite side). The formula used for finding the length of the line is, mc = (1/2)sqrt[2a2 + 2b2 - c2].

Height ha: This is the height (h) of the triangle using side a as the base. The formula used to find the height is, ha = 2 * (K / a), where K is the area of the triangle.

Height hb: This is the height (h) of the triangle using side b as the base. The formula used to find the height is, hb = 2 * (K / b), where K is the area of the triangle.

Height hc: This is the height (h) of the triangle using side c as the base. The formula used to find the height is, hc = 2 * (K / c), where K is the area of the triangle.

Vertex A coordinate: This is the coordinate used for vertex A. In order to plot the triangle for drawing, vertex A is always located at coordinate [0,0].

Vertex B coordinate: This is the coordinate used for vertex B. In order to plot the triangle for drawing, the y coordinate of vertex B is always 0. The x coordinate of vertex B is always equal to the length of side c.

Vertex C coordinate: This is the coordinate used for vertex C. The calculations used to find the x and y coordinates of vertex C are as follows:
ca = (b2 - a2 + c2) / (2 * c)
ch = sqrt[b2 - ca2]
cx2 = 0 + (ca * (c - 0)) / c
Cx = cx2 + (ch * ( 0 - 0 ) / c)
cy2 = 0 + (ca * (0 - 0)) / c
Cy = cy2 + (ch * ( c - 0 ) / c)

Centroid coordinate: This is the centroid coordinate based on the three vertex coordinates. The formula used is:
Centroid x = 1/3(Ax + Bx + Cx)
Centroid y = 1/3(Ay + By + Cy)

Circumcenter coordinate: This is the circumcenter coordinate based on the three vertex coordinates. The formula used is:
D = 2(BxCy - ByCx)
Ux = Cy(Bx2 + By2) - By(Cx2 + Cy2) / D
Uy = Bx(Cx2 + Cy2) - Cx(Bx2 + By2) / D

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