How to Get the Interior Angle of an Isosceles Triangle

An isosceles triangle has two equal sides.

In geometry or trigonometry courses, part of the curriculum includes measuring the interior angles of triangles. Problems that simulate symmetrical triangles such as a roof's slop employ isosceles triangles. An isosceles triangle has two sides of equal length. You can use this information, along with the side lengths, to determine all interior angles of an isosceles triangle.

Things You'll Need

• Scientific calculator

Instructions

1. Determine which angle is unequal. Because two sides have an equal length, their two opposite angles will be equal.

2. Let a and b represent the two equal sides, and let A and B represent the angles opposite these sides. Divide a by the side adjacent to B, usually the side from which the angle is measured. For example, a triangle with side lengths of 5, 5 and 3 would yield a result of 1.66.

3. Enter the value into your calculator and press the key labeled "tan-1." You will get the value for A.

4. Multiply A by 2.

5. Subtract the result from 180. The difference yields C, the third angle; all triangles on a flat plane have angle sums of 180.

References

• University of Minnesota: Conjectures in Geometry