How to find the bisector of a triangle | Education 2022

Cutters, surveyors, installers, and people in other professions must be able to divide an angle in half and calculate the length of a line drawn from the top to the other side.

How to find the bisector of a triangle
How to find the bisector of a triangle


Pencil tool Ruler Protractor Tables of sines and cosines Mathematical formulas and concepts: Bisector definition Sine and cosine theorems Bisector theorem


Step 1

Does it build a triangle of the required shape and size depending on what is given to you? The sides and the angle between them, three sides or two angles, and the side between them.

Designate vertices and sides with the traditional Latin letters A, B, and C. Vertices are indicated in uppercase, with opposite sides in lowercase. Mark the corners with Greek letters? J?

Use the sine and cosine theorems to find the dimensions of the triangle’s angles and sides.

Step 2

Remember the bisector definition. The bisector is a straight line that divides the angle in half. The bisector of a triangle divides the opposite side into two segments, which is equal to the ratio of the two adjacent sides of the triangle.

Draw the bisectors of the corners. The resulting segments are denoted by the names of the corners, written in lowercase, with a subscript l. Side c is divided into segments a and b with indexes l.

Find the lengths of the resulting line segments using the law of sines.

Step 3

Calculate the length of the bisector with the formula:

The length of the bisector is equal to the square root of the product of the segments by which the bisector divides the side opposite the angle, subtracted from the product of the adjacent sides.

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