This SSA triangle calculator tool helps you determine the possible solutions for a triangle when you know two sides and a non-included angle.

## SSA Triangle Calculator

This SSA (Side-Side-Angle) triangle calculator allows you to calculate the third side, one missing angle and the area of a triangle given two sides and an angle not between them.

### How to Use It

- Enter the lengths of sides
**a**and**b**. - Enter the measure of the angle
**C**in degrees (the angle opposite the side you wish to calculate). - Click
**Calculate**to see the results, including the length of the third side and the values of the other two angles.

### Explanation

For any given non-right triangle, if two sides and one non-included angle are known, the law of cosines can be used to find the length of the third side. The calculated side and one of the known sides together with the known angle then allows the law of sines to be used to find the other two angles of the triangle.

The law of cosines is given by: `c = sqrt(a² + b² - 2ab * cos(C))`

Once the third side is found, the law of sines is used to find the unknown angles: `A = asin((a * sin(C)) / c)`

and `B = 180 - C - A`

### Limitations

This calculator assumes that the input values create a viable triangle. Invalid inputs, such as nonpositive side lengths or angles greater than or equal to 180 degrees, are not handled by this calculator.

Also, in some cases, the SSA condition can produce two different valid triangles, known as the ambiguous case. This calculator assumes the solution is for the non-obtuse triangle.

## Use Cases for This Calculator

### Calculate the Third Side Length

Enter the lengths of two sides of a triangle and the measure of the included angle. Click the calculate button to find the length of the unknown side. This feature is useful when you know two sides and the angle between them and want to find the remaining side’s length.

### Determine if a Triangle is Possible

Input the lengths of two sides and the measure of the included angle. The calculator will verify if it’s possible to form a valid triangle with the provided measurements. It helps you quickly check the validity of a triangle based on the SSA condition.

### Calculate the First Angle

Provide the lengths of two sides and the length of the side opposite to the angle you wish to find. Click calculate to determine the value of the angle. Useful when you need to find an angle of a triangle using two sides and the side opposite to that angle.

### Switch between Degrees and Radians

Toggle between degrees and radians when entering the angle information. This feature lets you work with angle measurements conveniently in the unit of your preference. It enhances flexibility in input based on your calculations’ requirements.

### Clear Inputs with a Single Click

Reset all the input fields at once by clicking the clear button. Easily clear the information and start fresh when you want to perform new calculations without manually deleting individual values. This functionality ensures a quick and efficient way to erase all inputs.

### Responsive Design for Mobile Use

Experience seamless use on various devices, including smartphones and tablets, thanks to the responsive design. The calculator adapts to different screen sizes, providing functionality and ease of use across multiple platforms for on-the-go calculations.

### Display Error Messages for Invalid Inputs

Receive instant feedback with error messages if you input values that do not comply with the triangle inequality theorem. This feature helps you quickly identify and rectify any incorrect inputs, ensuring accurate calculations and valid results.

### Incremental Calculation Updates

Observe real-time updates on the calculated results as you input or modify the triangle’s measurements. The calculator dynamically adjusts and displays the outcomes without the need for manual refresh, enabling a smooth calculation process.

### Share Calculated Results Effortlessly

Share the calculated values with others by copying the result or a shareable link generated by the calculator. Easily communicate the triangle’s side lengths and angles for further analysis or collaboration, enhancing the calculator’s utility in sharing information.

### Save Time with Quick Access Buttons

Access commonly used functions like clear, calculate, and switch measurements quickly with dedicated buttons. These shortcuts streamline your interaction with the calculator, saving time and providing a user-friendly experience for efficient triangle calculations.