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Law of Sines Lesson 4.1

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2 Working with Non-right Triangles We wish to solve triangles which are not right triangles B A C a c b h View Sine Law Spreadsheet View Sine Law Spreadsheet

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3 Spreadsheet Exercise Note sine ratios for all angles 60° Change angle to 75°, record ratios Change side a to 20, record ratios Change side b to 5, record ratios What is smallest sin ratio you can get? What is largest? Why can you change the ratio with the angles all the same? Check out elegance point exercises

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4 Using the Sine Law If we know two angles and one side, we can solve the triangle Actually, if we know two angles, we know all three B A =23.5° C = 112° a c b = 216.75

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5 Using the Sine Law If we know two sides and an opposite angle We can solve the whole triangle Now how to find angle C and then side c? A C a =9.5 c b=15 B = 47°

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6 The Ambiguous Case (SSA) Given two sides and an angle opposite one of them, several possibilities exist No solution, side too short to make a triangle One solution, side equals altitude 20° 10 1 20° 10 3.42

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7 The Ambiguous Case (SSA) Two possible triangle could result (why?) One unique solution, the opposite side is longer than adjacent side 20° 10 5 A A' Solving for A could give either an acute or obtuse angle! 20° 10 13.42

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8 Try It Out Solve these triangles – watch for ambiguous case 28° 78° 44 32° 9.0 14

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9 Height of a Kite Two observers directly under the string and 30' from each other observe a kite at an angle of 62° and 78°. How high is the kite? 30 78° 62° ?

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10 Assignment Lesson 4.1 Page 298 Exercises 1 – 31 odd

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11 Elegance Exercises On the Sine Law spreadsheet Set both sides to 15 Manipulate angle Record at least 12 ordered pairs (angle, ratio) Plot them, determine what kind of function this is Determine possible function for the ordered pairs Set the angle to 75° Manipulate one other side Record at least 12 ordered pairs (side, ratio) Plot them, determine what kind of function this is Determine possible function for the ordered pairs Type up your findings in a neat format. Report your results with diagrams, complete sentences. Submit for extra points on next test

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Note 8– Sine Rule The “Ambiguous Case”

Note 8– Sine Rule The “Ambiguous Case”

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