Enter the length of the known side and the measures of the known angles into the calculator to determine the length of the missing side in an AAS triangle; this calculator can also evaluate any of the variables given the others are known.

Aas (Angle-Angle-Side) Formula

The following formula is used to calculate the length of the missing side in an Angle-Angle-Side (AAS) triangle:

a = (b * sin(A)) / sin(B)

Variables:

  • a is the length of the missing side
  • b is the length of a known side
  • A is the measure of the known angle (in radians)
  • B is the measure of the other known angle (in radians)

To calculate the length of the missing side in an AAS triangle, multiply the length of the known side by the sine of the known angle, and divide the result by the sine of the other known angle.

What is Aas (Angle-Angle-Side)?

AAS (Angle-Angle-Side) is a rule used to prove that two triangles are congruent. According to this rule, if two angles and the non-included side of one triangle are congruent to the corresponding two angles and non-included side of another triangle, then the two triangles are congruent. The term “non-included side” refers to the side that is not between the two angles. This rule is a shortcut derived from the ASA (Angle-Side-Angle) postulate, where the third sides and angles of the two triangles are proven to be congruent by the laws of geometry. The AAS rule is particularly useful in geometry problems where it is not immediately obvious that two triangles are congruent.

How to Calculate Aas (Angle-Angle-Side)?

The following steps outline how to solve an AAS (Angle-Angle-Side) problem:

  1. First, identify the two given angles in the triangle.
  2. Next, use the given angles to find the third angle of the triangle by subtracting the sum of the two given angles from 180 degrees.
  3. Then, determine the length of the side opposite to one of the given angles using the Law of Sines or any other applicable trigonometric formula.
  4. Finally, use the Law of Sines or any other applicable trigonometric formula to find the length of the remaining side or angle.

Example Problem:

Use the following variables as an example problem to test your knowledge:

Angle A = 45 degrees

Angle B = 60 degrees

Side c = 8 units