1. Non-Right Angle Trigonometry
   
TRIG-L4 Objectives: To solve side lengths and angles of non-right angle triangles.
Learning Outcome B-4

2. In right-angled triangles you work with angles from 0° to 90°.
If you increase one of the angles of a triangle to a value greater than 90°, the triangle can no longer be right angled (as the sum of angles of a triangle add to 180°). These are obtuse or non-right angle triangles. One angle of the triangle is greater than 90°.
Remember that when labeling triangles, capital letters are used for angles and lower-case letters are used for sides. Angle A is across from side a, B is across from b, and C is across from c.
Theory – Intro

3. Remember that when labeling triangles, capital letters are used for angles and lower-case letters are used for sides. Angle A is across from side a, B is across from b, and C is across from c. A b c C a B
Theory – Intro

4. To solve side lengths and/or angles of non-right angle triangles, you use either the Law of Cosines or the Law of Sines, depending on the type and amount of information you have.
Law of Cosines
Law of Sines
In PreCalculus you would substitute your values into the formulas shown above and solve for your unknown algebraically.
In Applied, we substitute our values into the Trig Calculator and interpret the output provided. Getting the correct answer depends on your ability to substitute into the correct part of the Calculator.
Theory – General Formulas

5. How to Use the Trig Calculator for Non Right-Angle Trig
When solving a missing side length on a Non-Right Angle Triangle, you need to have one of two situations:
1. If you know 2 sides of a triangle and the angle between them, use this part of the Calculator to find the third side length (this is Law of Cosines).
2. If you know two angles, and a side length across from one of the known angles, use this part of the Calculator to find the third side (Law of Sines).
Application – Solving for a Side Length

6. How to Use the Trig Calculator for Non Right-Angle Trig
When solving a missing angle measure on a Non-Right Angle Triangle, you need to have one of two situations:
1. If you know all 3 sides of a triangle, use this part of the Calculator to find a missing angle. The side length you call a must be across from the angle you are trying to solve A (this is Law of Cosines).
2. If you know two sides, and an angle across from one of the known sides, use this part of the Calculator to find the third side (Law of Sines).
Application – Solving for an Angle Measure

7. Pay careful attention to the side and angle labeling in the Calculator, both for inputs and outputs. Remember a is across from A, b is across from B, and c is across from C, always.
Careful – Substitution Errors

8. Study the diagram below.
Decide on a strategy to solve one missing value at a time.
Solve for all missing values.
Example 1

9. Solve Y by subtraction (180° – 80° – 40° = 60°)
Example 1 - Solution

10. Solve y using Z, z and Y. 60° Solve x using Z, z and X.
Example 1 - Solution

11. 23.4
60°
26.7
Example 1 - Solution