Basic Trigonometric Triangles

All on their own, angles are certainly very exciting. But put them into a triangle, and you've got icing on the cake. Triangles are one of the most frequently studied geometric figures. The angles that make up the triangle give them many of their characteristics.

Angles in triangles

A triangle always has three angles. The angles in a triangle have measures that always add up to 180 degrees — no more, no less.

A triangle named ABC has angles A, B, and C, and you can name the sides

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depending on which two angles the side is between. The angles themselves can be acute, obtuse, or right. If the triangle has either an obtuse or right angle, then the other two angles have to be acute.

Naming triangles by their shape

Triangles can have special names based on their angles and sides. They can also have more than one name — a triangle can be both acute and isosceles, for example. Here are their descriptions, and check out the pictures:

  • Acute triangle: A triangle where all three angles are acute.

  • Right triangle: A triangle with a right angle (the other two angles must be acute).

  • Obtuse triangle: A triangle with an obtuse angle (the other two angles must be acute).

  • Isosceles triangle: A triangle with two equal sides; the angles opposite those sides are equal, too.

  • Equilateral triangle: A triangle where all three side lengths are equal; all the angles measure 60 degrees, too.

  • Scalene triangle: A triangle with no angles or sides of the same measure.

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