Math 20-1 Chapter 2 Trigonometry Teacher Notes Math 20-1 Chapter 2 Trigonometry 2.3 The Sine Law

2.3 The Sine Law 30° Angle or ratio? 0.174 Angle or ratio? Math 20-1 Chapter 1 Sequences and Series 2.3 The Sine Law Trig Equations 30° Angle or ratio? 0.174 Angle or ratio? Angle or ratio? 2.3.1

? Solving Non-Right Triangles with Primary Trig Ratios Stan observes that the angle of elevation of a plane to be 510. At the same time, Paul observes it to be 340. The pilot used a range finder to determine that Stan is 190.85m from the plane and Paul is 265.24m from the plane. How far apart are Stan and Paul? (nearest m) 265.24 m 190.85 m Paul Stan 510 340 ? 2.3.2

? Solving with Primary Trig Ratios Alternate method: 510 340 A B C Stan Paul 265.24 m ? 190.85 m D Alternate method: Solve non-Right Triangle Total Distance = BD + CD Stan and Paul are 340 m apart 2.3.3

An oblique triangle is a triangle that does not contain a right angle. Using the definition of sine ratio: A B C b c a Isolate the variable h: h D Using the Transitive Property: Divide by bc Divide by sinBsinC 2.3.4

The Law of Sines For an oblique triangles or right triangles, when you are given SSA or ASA: a b c B C A 2.3.5

Proving Equivalence 30° 2 What do you notice about each ratio? 3 60° 1 60° 30° 2 What do you notice about each ratio? Would equivalence change if the reciprocals were written?

A S S ? or Solving with Primary Trig Ratios Alternate method: Solve non-Right Triangle 510 340 A B C Stan Paul 265.24 m ? 190.85 m Given: two angles and one side or two sides and an angle opposite one of the given sides S S 950 How would the solution be affected if you would have chosen Stan and Paul are 340 m apart or 2.3.6

Applying the Law of Sines (nearest 100th for lengths, 10th for angles) 600 c 1800- (750 + 450) = 600 c = 12.25 2.3.7

Assignment Suggested Questions Page 97: 10, 15 Page 108: 1a, 2a, 3a, 5a, 11, 13, 19 2.3.8