Allen WolmerSandy Springs, Georgia, US,

April 29, 2015

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Student Resources

- Mathematics > General
- Mathematics > Geometry

- Grade 9
- Grade 10

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Table of Contents

- Proof: Law of Sines
- Law of Cosines
- Law of cosines
- Proving Law of Sines and Cosines
- Oblique Triangles Law of Sines
- Ambiguous Case for Law of Sines
- Law of Cosines
- Law of cosines
- Applications of Law of Sines and Cosines
- Law of Sines - Application/Word Problem, Ex 1
- Law of Sines - Application / Word Problem, Ex 2
- Law of Sines - Application/Word Problem, Ex 3
- Law of Cosines, Example 1
- Law of Cosines, Example 2
- The Law of Cosines, Example 3
- Law of Cosines, Example 4
- Law of Cosines, Example 5
- Law of Cosines, Example 6
- Trigonometry - Oblique Triangles

Student Resources

A simple proof of the Law of Sines

A Youtube video from Khan Academy

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Introduce and do examples of solving oblique triangles using the law of cosine.

A Youtube video from ProfRobBob.

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Introduction to the law of cosines to solve for a side of a triangle when 2 sides and an angle are known.

A Youtube video from Khan Academy

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Step by step proof of both the Law of Sines and Law of Cosines for general triangles.

A Youtube video from Patrick Dugas

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Introduce the Law of Sine and go over a couple of examples where there is one unique triangle. Finish with an example of finding area of an oblique triangle.

A Youtube video from ProfRobBob.

Note: There may be a short ad at the beginning

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Introduce solving oblique triangles when the information given is in the SSA form...or the ambiguous case. In this setting there may be one solution, two solutions, or none at all.

A Youtube video from ProfRobBob.

Note: There may be a short ad at the beginning

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Introduce and do examples of solving oblique triangles using the law of cosine.

A Youtube video from ProfRobBob.

Note: There may be a short ad at the beginning

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Introduction to the law of cosines to solve for a side of a triangle when 2 sides and an angle are known.

A Youtube video from Khan Academy

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Four examples to help you understand how to solve some of your word problems that require Law of Sine and/or Cosine.

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Law of Sines - Application/Word Problem, Ex 1. In this Youtube video from patrickJMT, do a word/application problem that involves using the law of sines.

There may be a short as at the beginning.

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Law of Sines - Application/Word Problem, Ex 2. Another word/application problem that involves using the Law of SInes.

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Law of Sines - Application/Word Problem, Ex 3. Another word/application problem that involves using the Law of Sines.

Note: There may be a short ad at the beginning.

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The Law of Cosines, Example 1. In this Youtube video from patrickJMT, give the formula for the Law of Cosines and use it to find the missing side length of a triangle.

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The Law of Cosines, Example 2. In this Youtube video from patrickJMT, give the formula for the Law of Cosines and use it to find the missing side length of a triangle.

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The Law of Cosines, Example 3. In this Youtube video from patrickJMT, give the formula for the Law of Cosines and use it to find the value of a missing angle.

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The Law of Cosines, Example 4. In this Youtube video from patrickJMT, use the law of cosines to help deduce an angle between the flightpath of two planes!

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Law of Cosines, Example 5. A Youtube video from patrickJMT, giving another example of finding the missing length of a triangle using the Law of Cosines.

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Law of Cosines, Example 6. In this Youtube video from patrickJMT, find how far a person is from a house by knowing that person's distance to someone else and the angle formed between them and the house.

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Trigonometry - Oblique Triangles from MathBitsNotebook.com

A collection of lessons and practice examples with answers:

LESSONS

Area of Triangle (formulas, derive formula, sine of an obtuse angle)

Law of Sines (oblique, ASA, AAS, examples, deriving the formula)

Law of Sines - Ambiguous Case (SSA, examples, summary, what to look for)

Law of Cosines (SAS, SSS, facts to remember, deriving the formula, examples)

Law of Cosines - Ambiguous Case (SSA, quadratic formula, examples, summary)

Applications with Navigation and Vectors

PRACTICE:

PRACTICE

Practice with Area of Triangles Using Trigonometry

Practice Law of Sines

Practice with Law of Cosines

Practice with Navigation and Vectors

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