TGT - Trigonometry of General Triangles Module Overview

Trigonometry of General Triangles Module Overview

Introduction

Prior to this Module, you have dealt mostly with right triangles during your mathematical career. However, in this module we will explore non-right, or oblique, triangles! You can still use trigonometry to solve them, but not by your traditional trigonometric ratios. Oblique triangles are often used in navigation and estimating distances - read on to see how we will solve oblique triangles!

Essential Questions

How can I calculate the area of any triangle given only two sides and a non-included angle?
How can I apply trigonometric relationships to non-right triangles?

Trigonometry of General Triangles Key Terms

The following key terms will help you understand the content in this module.

Altitude of a triangle - The perpendicular distance between a vertex of a triangle and the side opposite that vertex.

Included Angle - The angle between two given sides of a triangle.

Law of Cosines - equation image indicator $LaTeX: c^2=a^2+b^2-2ab\cdot\cos C$ $c^2=a^2+b^2-2ab\cdot\cos C$

Law of Sines - equation image indicator $LaTeX: \frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}$ $\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}$

Oblique Triangle - A triangle that is not a right triangle.

Angle of Elevation - The angle of elevation of an object as seen by an observer is the angle between the horizontal and the line from the object to the observer's eye (the line of sight).

Angle of Depression - The angle below horizontal that an observer must look to see an object that is lower than the observer.

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