Relationships in Trigonometry
Trigonometry is the study of relationships between angles and sides of a triangle and utilizes a handful of equations to describe these relations.
In terms of the relationship between angles, remember that all angles in a triangle will total to 180°. In a right triangle, one of these angles will be 90°. That being said, if we know two angles in a triangles, and want to find the third angle, simply subtract both angles from 180 to find the third angle.
For example: If a right triangle has a known angle of 35°, what is the last angle?
In terms of the relationship between sides, we’ll need to familiarize ourselves with the terminology that will also come in handy later on in this module. For now, the most important term to know is hypotenuse. In a right-angle triangle, the hypotenuse is the line connecting the perpendicular sides of a right triangle together. If we know two side lengths of a triangle and wanted to figure out the third side length, we can figure it out using the Pythagorean theorem.
The Pythagorean theorem equation is given above. By identifying the legs and the hypotenuse, we can plug, rearrange, and solve for any third unknown side length (Refer to Module 7: Algebra for rearranging).
Exploiting the relationship between sides and angles together will require ratios that can solve for unknown values of a right triangle. For this, we’ll first need to understand what each side is relative to a specific angle. Let’s consider one angle as the reference point, (theta).
The leg involved in forming the angle is known as the adjacent side. The leg on the opposite side of the triangle is known as the opposite side. The hypotenuse remains as the hypotenuse.
Using a reference point, ratios and trigonometric functions can be coupled for solving unknowns in a right triangle.
