Triangle Area from Two Angles and Interior Side

The Area of a Triangle Based on Two Angles and the Interior Side calculator computes the area of a triangle given the measurement of two of the triangle’s angles and the dimension of the interior side.

INSTRUCTIONS:  Choose units and enter the following: :

• (α) Angle 1
• (β)  Angle 2
• (c) Length of Side in between them.

Area of a Triangle (A): The calculator computes the area of the triangle in square meters (m²).  However, this can be automatically converted to other area units (e.g. square feet) via the pull-down menu.

The Math / Science

The formula for the area of a triangle based on two angles and the length of the side in between them is:

     `A = (c^2 * sin(β) * sin(α)) / (2 * sin( 2π -  α - β)`

where:

• A = Area of triangle
• α = one interior angle
• β = second interior angle
• c = length of side between angles

A triangle is a polygon with three sides, three vertices (corners), and three angles. Triangles can be classified based on the lengths of their sides and the measures of their angles as follows:

By Side Lengths:

• Equilateral Triangle: All three sides are equal in length.
• Isosceles Triangle: Two sides are equal in length.
• Scalene Triangle: All three sides have different lengths.

By Angle Measures:

• Acute Triangle: All three angles are less than 90 degrees.
• Right Triangle: One angle is exactly 90 degrees.
• Obtuse Triangle: One angle is greater than 90 degrees.

The sum of the interior angles of any triangle always adds up to 180 degrees. 

Triangle Calculators

• Area of Triangle (base and height)
• Area of Triangle (two sides and interior angle)
• Area of Triangle (two angles and interior side)
• Area of Triangle (three sides)
• Area of Equilateral Triangle
• Area of Triangle (three points)
• Height of Triangle
• Width of Triangle
• Triangle Perimeter
• Interior Angle of a triangle based on the length of three sides
• Semi-perimeter of a triangle
• Area of Circle Within a Triangle
• Area of Circle Around a Triangle
• Area between two vectors
• Triangle Volume