Elementary Algebra
Introduction to Algebra Linear Equations and Inequalities Functions and Graphs I Lines and thier Graphs Linear Systems Exponents & Polynomials
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Precalculus I / College Algebra
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Precalculus II / Trigonometry
The Six Trigonometric Functions Right Triangle Trigonometry Circular Functions Graphs of Trigonometric Functions Trigonometric Identities Trigonometric Equations Oblique Triangles and the Laws Vectors Complex, Parametric, and Polar Forms
Calculus I
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Calculus II
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Calculus III

Course: Trigonometry
Topic: Oblique Triangles and the Laws
Subtopic: Area of a Triangle

Overview

Remember the area of a triangle formula A=1/2bh? This formula works on both right and oblique triangles, but you have to know the length of the altitude (h) of the triangle. In the triangles we have been working with lately, we aren't given the altitude, just sides and/or angles. So, new area formulas would be useful.

The common A=1/2bh formula is actually a special case of the area of a triangle formula A=1/2ab*sin gamma where gamma is the included angle between sides of length a and b. This formula can be used to find the area of an oblique triangle given SAS.

To find the area of an oblique triangle given SSS, use Heron's Area Formula, A=sqrt(s(s-a)(s-b)(s-c)) where s is the semiperimeter of the triangle. This formula has an interesting history and extends into higher dimensions. See the supplementary resources below for more information.

Objectives

By the end of this topic you should know and be prepared to be tested on:

• 7.4.1 Find the area of an oblique triangle given SSS via Heron's Area Formula
• 7.4.2 Find the area of an oblique triangle given SAS

Terminology

Terms you should be able to define: semiperimeter s=1/2(a+b+c)
Heron's Area Formula A=sqrt(s(s-a)(s-b)(s-c))
Area formula A=1/2ab*sin gamma

Mini-Lectures and Examples

Supplementary Resources

rev. 2020-11-09