Law of Sines Lesson 4 1 Working with

  • Slides: 11
Download presentation
Law of Sines Lesson 4. 1

Law of Sines Lesson 4. 1

Working with Non-right Triangles ¡ We wish to solve triangles which are not right

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

Spreadsheet Exercise Note sine ratios for all angles 60° ¡ Change angle to 75°,

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 ¡ 3

Using the Sine Law ¡ If we know two angles and one side, we

Using the Sine Law ¡ If we know two angles and one side, we can solve the triangle l Actually, if we know two angles, we know C = 112° all three a b = 216. 75 A =23. 5° c B 4

Using the Sine Law ¡ If we know two sides and an opposite angle

Using the Sine Law ¡ If we know two sides and an opposite angle l We can solve the whole triangle C a =9. 5 b=15 A ¡ c Now how to find angle C and then side c? B = 47° 5

The Ambiguous Case (SSA) ¡ Given two sides and an angle opposite one of

The Ambiguous Case (SSA) ¡ Given two sides and an angle opposite one of them, several possibilities exist l No solution, side too short to make a triangle l One solution, side equals altitude 1 10 20° 10 3. 42 20° 6

The Ambiguous Case (SSA) l Two possible triangle could result (why? ) 10 5

The Ambiguous Case (SSA) l Two possible triangle could result (why? ) 10 5 20° One unique solution, the opposite side is longer than adjacent side 5 A A' l Solving for A could give either an acute or obtuse angle! 10 13. 42 20° 7

Try It Out ¡ Solve these triangles – watch for ambiguous case 9. 0

Try It Out ¡ Solve these triangles – watch for ambiguous case 9. 0 44 78° 28° 14 32° 8

Height of a Kite ¡ Two observers directly under the string and 30' from

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? ? 78° 62° 30 9

Assignment Lesson 4. 1 ¡ Page 298 ¡ Exercises 1 – 31 odd ¡

Assignment Lesson 4. 1 ¡ Page 298 ¡ Exercises 1 – 31 odd ¡ 10

Elegance Exercises On the Sine Law spreadsheet ¡ Set both sides to 15 l

Elegance Exercises On the Sine Law spreadsheet ¡ Set both sides to 15 l l ¡ Type up your findings in a neat format. Report your results with diagrams, complete sentences. Submit for extra points on next test 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° l l 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 11