6.1+-+Law+of+Sines

Home >> Precalculus >> ** 6.1 Law of Sines **


 * Law of Sines: **
 * 1) Useful for solving triangles:
 * 2) 2 angles and any side: AAS, ASA
 * 3) 2 sides and an angle opposite them: SSA (aka the ambiguous case)
 * 4) Single solution, no solution (an impossible triangle), 2 solutions
 * 5) Useful for finding the area of an oblique (non right) triangle

**Book**: Pages 392-397
 * Homework**: p. 398 1-8 all, 27, 28


 * Teaching method:**
 * 1) Review common triangles: 60-60-60, 30-60-90 and 45-45-90 and how you can find side lengths without anything fancy.
 * 2) Review right triangles solvable with Pythagorean Theorem.
 * 3) Review right triangles solvable with trig ratios - sine, cosine, and tangent.
 * 4) What if you had a 3, 3, 3 triangle?
 * 5) What if you had a 3, 4, 5 triangle? Could you determine at least 1 angle easily? How about the other 2 angles? Find them using trig.
 * 6) What if you had a 5, 12, 13 triangle? Could you ...? Find them using trig.
 * 7) What if it was 3, 4, and 5.1? What about 3, 4, 4.9? - The idea of using what you know + common sense.
 * 8)  Approximating a solution using a sketch: Problem 1: 40°, 50 °, and side between  is 10 units. Find other sides by making a careful sketch (but do students have graph paper, a protractor and a ruler?).
 * 9) Same problem solved with GeoGebra or SMART Notebook or Wolfram Alpha.
 * 10) GeoGebra: ASA - GeoGebra, Ambiguous case - GeoGebra
 * 11) Wolfram Alpha: asa 30deg 10feet 60deg
 * 12) Solve using Law of Sines.

media type="youtube" key="APNkWrD-U1k?rel=0" height="240" width="320"
 * Proof of the Law of Sines - Khan Academy **


 * Video - MathTV**: Practice Problems worked


 * GeoGebra interactivity** for the ambiguous case: Fishing rod