# ALEX Classroom Resource

## Precalculus and Advanced Topics Module 4, Topic B: Trigonometry and Triangles

Classroom Resource Information

Title:

Precalculus and Advanced Topics Module 4, Topic B: Trigonometry and Triangles

URL:

Content Source:

EngageNY
Type: Lesson/Unit Plan

Overview:

Students derive sophisticated applications of the trigonometric functions in Module 4, Topic B including the area formula for a general triangle, the law of sines, the law of cosines, and Heron’s formula. They use previous knowledge and apply their understanding of the Pythagorean theorem and oblique triangles to discover these formulas while analyzing patterns. Finally, as students investigate force diagrams and paths across rivers, they solve survey and elevation problems and revisit vectors.

Note: This module is identified as Precalculus and Advanced Topics in the EngageNY curriculum. It also corresponds to the Geometry Alabama Course of Study.

Content Standard(s):
 Mathematics MA2015 (2016) Grade: 9-12 Geometry 22 ) (+) Prove the Law of Sines and the Law of Cosines and use them to solve problems. [G-SRT10] Mathematics MA2015 (2016) Grade: 9-12 Geometry 23 ) (+) Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles (e.g., surveying problems, resultant forces). [G-SRT11] Mathematics MA2015 (2016) Grade: 9-12 Precalculus 35 ) (+) Derive the formula A = (1/2)ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side. (Apply formulas previously derived in Geometry.) [G-SRT9] (Alabama)
Tags: area, Herons formula, law of cosines, law of sines, oblique triangles, Pythagorean Theorem, triangle, trigonometry
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