Geometric Equations Involving Triangles
One of the first theorems that we learn in Geometry is the Pythagorean Theorem which explains the relationship of the sides of a right triangle. The Pythagorean Theorem states that the square of the hypotenuse or the longest side of a right triangle is equal to the sum of the square of the two remaining sides. This relationship can be written in the formula a² + b² = c².
This equation is very important in solving math problems involving right triangles. When given a right triangle with two known sides, we can use the said formula to look for the third side of the triangle. However, the Pythagorean Theorem is only applicable to right triangles which have an angle of 90 degrees. For acute triangles having angles of less than 90 degrees, and obtuse triangles which have angles of more than 90 degrees, other formulas may be necessary. The cosine formula would be more applicable since it takes into account the angles of the triangle.
The Law of Cosines explains the relationship of a triangle’s angles and sides. It is almost the same with the Pythagorean Theorem except that it deals with acute and obtuse angles. The equation for the Law of Cosine is written as a² = b² + c² – 2bc cos ? wherein the unknown side ‘a’ is opposite angle ?. So, in order to get the measurement of one side of a triangle, you would have to know the measurement of the other two sides as well as the angle opposite the unknown side of the triangle.
The Pythagorean Theorem and Law of Cosines deal with the relationships between sides and angles of a triangle. These geometry formulas are important in many Mathematical problems and they have real life applications as well. They are used in triangulation and trilateration which are processes used in identifying absolute and relative locations using fixed points at either ends of a baseline.