Unit 07 · Lesson 03 · Week 20 · Triangle Trigonometry, Bearings & Applications
Law of Cosines
Solve right and oblique triangles with trigonometric ratios, Laws of Sines and Cosines, area formulas, bearings, and uncertainty analysis. In this lesson, the central focus is law of cosines. Learners move among symbolic, graphical, numerical, and contextual evidence rather than relying on one representation alone.
Learning intentions
- Interpret the defining quantities and notation used in law of cosines.
- Construct or analyze at least two representations related to law of cosines.
- Show symbolic work with correct domains, units, intervals, or angle measures.
- Explain why the selected method is valid and check the result against another representation.
Essential question
How do right-triangle ratios and oblique-triangle laws solve measurement, navigation, survey, and design problems?
Multiple-representation model
Solve right and oblique triangles with trigonometric ratios, Laws of Sines and Cosines, area formulas, bearings, and uncertainty analysis.
\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}c^2=a^2+b^2-2ab\cos CK=\frac12ab\sin C
Worked reasoning
Misconception check: SSA may produce zero, one, or two triangles; a calculator angle alone does not settle the ambiguous case.
Communication and reasoning
Write a complete response that identifies the representation used, shows the symbolic steps, interprets parameters or units, and verifies the conclusion with a second representation or reasonableness check.
Khaemenes Academy · Open-Age Precalculus
Law of Cosines
Analyze, calculate, graph, or justify each result. Show reasoning, intervals, units, and calculator evidence when used.
Name
Date
In a right triangle, opposite=6 and hypotenuse=10. Find sin θ.
Given a=7, A=35°, B=62°, find angle C.
Which law fits SAS data?
Find c when a=5, b=8, C=60°.
Find the area with a=10, b=12, C=30°.
A bearing of N35°E corresponds to what standard compass description?