Kinds of Triangles in Trigonometry
The study of trigonometry is built upon the study of geometry and algebra. As such, the triangles used in trigonometry are the same ones first learned about in geometry class. There are three types of triangles based on the length of their sides. There is also one special triangle that is the most commonly used in solving trigonometry problems, the right triangle.
Other People Are Reading
-
Equilateral Triangles
-
Equilateral triangles are essentially what the name implies. They have equal lateral sides, meaning the length of each side is the same. With equilateral triangles, all the angles of the triangle are acute, meaning the angle measures less than 90 degrees. This kind of triangle can also be called an "acute triangle." In plane geometry, the sum of the angles of any kind of triangle always equals 180 degrees.
Isosceles Triangles
-
In an isosceles triangle, two of the sides are the same length. An isosceles triangle, as with an equilateral triangle, can be an acute triangle. However, it can also be an obtuse triangle if one of the angles is greater than 90 degrees. While an acute triangle has all three angles less than 90 degrees, in an obtuse triangle, only one angle is greater than 90 degrees. Because the sum of angles always equals 180 degrees, there is never more than one angle greater than or equal to 90 degrees, at least not in flat-plane geometry.
-
Scalene Triangles
-
The third kind of triangle is the scalene triangle in which no two sides are the same length. Scalene triangles can be acute or obtuse. With a scalene triangle, the greater the difference in the length of the sides, the more likely the triangle will be obtuse.
The Right Triangle
-
The right triangle is a special triangle and the one most often dealt with in trigonometry problems. The right triangle can be isosceles or scalene. The two sides forming the right angle --- the 90-degree angle --- are the legs and the longest, third side is the hypotenuse. The right triangle is handy in calculating the sine, cosine and tangent. The sine of one of the acute angles is calculated by creating a fraction using the measure of the opposite leg over the hypotenuse. Cosine is the adjacent leg over the hypotenuse while tangent is the opposite leg over the adjacent leg.
-
References
- Photo Credit PhotoObjects.net/PhotoObjects.net/Getty Images
