To calculate the missing side using the AAS method, multiply the known side by the sine of the known angle opposite the missing side. Then, divide by the sine of the angle opposite the known side.

## AAS Calculator

Enter all but one value to calculate the unknown variable

The **AAS Calculator** is used to find the unknown side of a triangle when you are given two angles and one side that is not between them. This method uses the **Law of Sines**, which allows you to calculate the unknown side when two angles and a side are known.

### Formula:

Contents

The AAS formula is:

**a = (b × sin(A)) / sin(B)**

Where:

**a**is the unknown side,**b**is the known side,**A**and**B**are the known angles.

The **AAS rule** helps solve triangles when two angles and one non-included side are known. It is particularly useful in trigonometry and geometry for finding the missing sides and angles of a triangle.

**How to Calculate ?**

- Multiply the known side (b) by the sine of the angle opposite the unknown side (sin(A)).
- Divide the result by the sine of the angle opposite the known side (sin(B)).

**Solved Calculations:**

**Example 1:**

Calculation |
Instructions |
---|---|

Given: b = 10, A = 30°, B = 45° |
Start with the known side and angles. |

a = (10 × sin(30°)) / sin(45°) | Use the formula to find the unknown side. |

a = (10 × 0.5) / 0.7071 | Calculate the sine values. |

a = 5 / 0.7071 | Divide the results. |

a ≈ 7.07 |
The length of side a is approximately 7.07. |

**Answer:** The unknown side **a** is approximately **7.07**.

**Example 2:**

Calculation |
Instructions |
---|---|

Given: b = 15, A = 40°, B = 70° |
Start with the known side and angles. |

a = (15 × sin(40°)) / sin(70°) | Use the formula to find the unknown side. |

a = (15 × 0.6428) / 0.9397 | Calculate the sine values. |

a = 9.642 / 0.9397 | Divide the results. |

a ≈ 10.26 |
The length of side a is approximately 10.26. |

**Answer:** The unknown side **a** is approximately **10.26**.

**What is Angle – Angle – Side (AAS) Calculator ?**

The **AAS (Angle-Angle-Side) Calculator** is a helpful tool for solving triangles when you know two angles and one side. This method is useful in various fields, including geometry, engineering, and architecture.

To use the AAS calculator, you start by entering the measures of the two known angles and the length of the side that is not between them. The calculator will then provide the measures of the remaining angles and the lengths of the other sides.

The AAS rule states that if you have two angles and a non-included side, you can determine the other angles and sides of the triangle. This is because the sum of the angles in any triangle is always 180 degrees. Once you have two angles, you can easily find the third angle.

Understanding how to use the **law of sines** can also help when solving AAS triangles. This law relates the sides of a triangle to the sines of its angles, making it a powerful tool for finding missing values.

**Final Words:**

For more complex calculations, the AAS calculator can work in tandem with other calculators, such as the **ASA** and **SAS** calculators. Whether you’re a student learning geometry or a professional needing to solve triangles for a project, the AAS calculator simplifies the process and enhances your accuracy.