Lesson 2
1. Lesson 2
1.4. Explore
Module 1: Trigonometry
Explore
The relationship you discovered above in the Try This 2 and Share 2 activities is called the sine law and is valid for all triangles, including both right triangles and oblique triangles. It is usually written in the following way:
This is a short-hand way of writing three separate equations:
This mathematical expression could be written in words as “The length of a side divided by the sine of the opposite angle is the same for all side-angle pairs in any triangle.” The animation Sine Law Illustrator shows this pictorially.
This formula reflects how mathematicians typically label triangles: sides are named with lowercase letters and angles are named with uppercase letters. Sides and their opposite angles are named with the same letter—for example, b and B.
You may find it helpful to view How to Label a Triangle.
You may want to add the sine law to your Formula Sheet document. Remember to save your updated Formula Sheet to your course folder.