Triangle calculator ASA

Please enter the side of the triangle and two adjacent angles

The ASA (Angle-Side-Angle) theorem is a statement in geometry that states that if two angles of a triangle are equal to two angles of another triangle and the side between those angles is common in both triangles, then the triangles are congruent.

To calculate the missing information of a triangle when given the ASA theorem, you can use the known angles and side lengths to find the remaining side lengths and angles.

If you know the measures of two angles (A and C) and the length of one side (b) between them, you can use the Law of Cosines to find the length of the remaining sides (a and c) as:

a2 = b2 + c2 - 2bc * cos(A)

c2 = a2 + b2 - 2ab * cos(C)

Once you have the length of the two remaining sides, you can use the Law of Sines to find the measure of the angle (B) that is not given as:

a/sin(A) = b/sin(B) = c/sin(C) = 2R

Where R is the circumradius of the triangle

You can also use the given angles and side length to find the area of the triangle using Heron's formula or using trigonometric functions like Sin or Cos.
It's important to note that you need to have the measures of two angles and one side to use this theorem. If you have only one angle and one side, it would not be possible to determine the triangle completely.

If you know one side, adjacent, and opposite angles use the AAS calculator.

Triangle ASA theorem math problems:

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Look also at our friend's collection of math problems and questions:

See triangle basics on Wikipedia or more details on solving triangles.