Mastering Included Angle Calculations: Formulas and Tips for Finding Angles Between Two Line Segments and in Triangles

Included Angle

The angle between two sides.

The included angle is the angle formed between two line segments that share a common endpoint. To find the included angle, you can use the formula:

included angle = arccos [(a · b) / (|a| |b|)]

where a and b are vectors representing the line segments.

Alternatively, you can use the law of cosines to find the included angle in a triangle:

cos(C) = (a^2 + b^2 – c^2) / (2ab)

where C is the angle between sides a and b, and c is the length of the side opposite angle C.

It is important to note that the included angle is always measured in radians, not degrees. To convert from radians to degrees, you can use the formula:

angle in degrees = (angle in radians) x (180 / pi)

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