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M1410601

# M1410601 - (Section 6.1 The Law of Sines 6.01 CHAPTER 6...

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(Section 6.1: The Law of Sines) 6.01 CHAPTER 6: ADDITIONAL TOPICS IN TRIG SECTION 6.1: THE LAW OF SINES PART A: THE SETUP AND THE LAW The Law of Sines and the Law of Cosines will allow us to analyze and solve oblique (i.e., non-right) triangles, as well as the right triangles we have been used to dealing with. Here is an example of a conventional setup for a triangle: There are 6 parts: 3 angles and 3 sides. Observe that Side a “faces” Angle A , b faces B , and c faces C . (In a right triangle, C was typically the right angle.) When we refer to a , we may be referring to the line segment BC or its length. The Law of Sines For such a triangle: a sin A = b sin B = c sin C Equivalently: sin A a = sin B b = sin C c

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(Section 6.1: The Law of Sines) 6.02 PART B: WHAT MUST BE TRUE OF ALL TRIANGLES? We assume that A , B , and C are angles whose degree measures are strictly between 0 and 180 . The 180 Rule The sum of the interior angles of a triangle must be 180 . That is, A + B + C = 180 . The Triangle Inequality The sum of any two sides (i.e., side lengths) of a triangle must exceed the third. That is, a + b > c , b + c > a , and a + c > b . Think: Detours. Any detour in the plane from point A to point B , for example, must be longer than the straight route from A to B . Example: There can be no triangle with side lengths 3 cm, 4 cm, and 10 cm, because 3 + 4 > 10 . If you had three “pick-up” sticks with those lengths, you could not form a triangle with them if you were only allowed to connect them at their endpoints. The “Eating” Rule For a given triangle, larger angles face (or “eat”) longer sides. You can use this to check to see if your answers are sensible.
(Section 6.1: The Law of Sines) 6.03 PART C: EXAMPLE Example Given: B = 40 , C = 75 , b = 23 ft.

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M1410601 - (Section 6.1 The Law of Sines 6.01 CHAPTER 6...

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