Home » Simplify your calculations with ease. » Mathematical Calculators » AAS (Angle-Angle-Side) Calculator Online

# AAS (Angle-Angle-Side) Calculator Online

The AAS (Angle-Angle-Side) calculator is a useful tool for determining the unknown side or angles in a triangle when two angles and one side not between them are given. This tool is essential in geometry, construction, and some areas of engineering where complete measurements of a triangle are not directly possible.

## Formula of AAS (Angle-Angle-Side) Calculator

The process to use the AAS calculator involves trigonometric principles, explained in a step-by-step manner:

1. Identify the Known Angles and Side:
• Assume A and B are the known angles.
• Let a be the known side, which is opposite angle A.
2. Calculate the Third Angle:
• Since the sum of all angles in a triangle is 180 degrees, the third angle, C, is calculated as: C = 180 degrees – A – B
3. Use the Law of Sines to Find the Other Sides:
• According to the Law of Sines, the relationship between the sides of a triangle and the sines of its angles is as follows: a / sin(A) = b / sin(B) = c / sin(C)
• To find side b: b = (a * sin(B)) / sin(A)
• To find side c: c = (a * sin(C)) / sin(A)

This method allows you to calculate any missing dimensions of a triangle when two angles and one side are known, making it a powerful tool for various practical applications.

## Quick Reference Table for Common AAS Calculations

Below is a table designed to offer a quick reference for those who frequently use the AAS calculator. It includes examples of common triangle configurations, specifying two angles and showing the calculated side lengths assuming a base side length of 1 unit for simplicity.

This table can be used as a base for calculation, where the side lengths (b and c) can be scaled up or down depending on the actual length of side a in your specific problem.

## Example of AAS (Angle-Angle-Side) Calculator

Consider a triangle where angles A and B are know to be 40 degrees and 60 degrees, respectively. The side a opposite angle A is know to be 5 cm. Here’s how you would use the AAS calculator:

1. Calculate the third angle:
• C = 180 degrees – 40 degrees – 60 degrees = 80 degrees
2. Use the Law of Sines to find the other sides:
• For side b:
• b = (5 cm * sin(60 degrees)) / sin(40 degrees) = (5 cm * 0.866) / 0.642 = approximately 6.75 cm
• For side c:
• c = (5 cm * sin(80 degrees)) / sin(40 degrees) = (5 cm * 0.985) / 0.642 = approximately 7.67 cm