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Chapter 6 Investigating Non-Right Triangles as Models for Problems: 6.3 Investigating the Sine Law

Chapter 6 Investigating Non-Right Triangles as Models for Problems: 6.3 Investigating the Sine Law. 6.3 Investigating the Sine Law. Goals for Today: Learn one of the ways that we can find unknown sides and angles in a non-right angle triangle. 6.3 Investigating the Sine Law. Minds On:

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Chapter 6 Investigating Non-Right Triangles as Models for Problems: 6.3 Investigating the Sine Law

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  1. Chapter 6 Investigating Non-Right Triangles as Models for Problems: 6.3 Investigating the Sine Law

  2. 6.3 Investigating the Sine Law Goals for Today: • Learn one of the ways that we can find unknown sides and angles in a non-right angle triangle

  3. 6.3 Investigating the Sine Law Minds On: • Sine Law Investigation textbook p.546 • I will handout graph paper and protractors • What conclusion do you draw?

  4. 6.3 Investigating the Sine Law • If we have a non-right angle triangle, we can’t use the primary trig ratios to find an unknown side or angle • In this case*, we can use the Sine Law to solve for an unknown angle or side if we are given: • 2 sides and one angle across from a known side, or • 2 angles and any side • *The Sine law will work in right angle triangles

  5. 6.3 Investigating the Sine Law • The Sine Law is: use this if solving for a side The small letters represent sides The large letters represent angles You work with two out of the three ratios

  6. 6.3 Investigating the Sine Law • The Sine Law is also: use this if solving for The small letters represent sides The large letters represent angles You work with two out of the three ratios

  7. 6.3 Investigating the Sine Law – Given 2 Sides and an Angle Across from a Known Side Ex. 1 Find angle C A 29.5cm 37.1cm C 44° B

  8. 6.3 Investigating the Sine Law – Given 2 Sides and an Angle Across from a Known Side Ex. 1 Find angle C A 29.5cm 37.1cm C 44° Angle B is across from a known side... B

  9. 6.3 Investigating the Sine Law – Given 2 Sides and an Angle Across from a Known Side Ex. 1. Find angle C in triangle ABC As with similar triangles, we need 3 out of 4 to be able to find the missing side or angle

  10. 6.3 Investigating the Sine Law – Given 2 Sides and an Angle Across from a Known Side Ex. 1. Find angle C in triangle ABC As with similar triangles, we need 3 out of 4 to be able to find the missing side or angle

  11. 6.3 Investigating the Sine Law – Given 2 Sides and an Angle Across from a Known Side

  12. 6.3 Investigating the Sine Law – Given 2 Sides and an Angle Across from a Known Side

  13. Humour Break

  14. 6.3 Investigating the Sine Law – Given 2 Angles and any Side X 88° y z=3 cm 25° Z Y x

  15. 6.3 Investigating the Sine Law – Given 2 Sides and an Angle Across from a Known Side Ex. 2. Find side x and find side y in triangle XYZ *Found missing angle by using 180° rule

  16. 6.3 Investigating the Sine Law – Given 2 Sides and an Angle Across from a Known Side Ex. 2. Find side x and find side y in triangle XYZ *Found missing angle by using 180° rule

  17. 6.3 Investigating the Sine Law – Given 2 Angles and any Side

  18. 6.3 Investigating the Sine Law – Given 2 Angles and any Side and

  19. 6.3 Investigating the Sine Law – Given 2 Angles and any Side

  20. 6.3 Investigating the Sine Law – Given 2 Angles and Any Side Ex. 3 Find the length side a and side b A b 27.2cm 43° C 72° a B

  21. 6.3 Investigating the Sine Law – Given 2 Angles and any Side Ex. 1. Find side a and find side b in triangle ABC

  22. 6.3 Investigating the Sine Law – Given 2 Angles and any Side Ex. 1. Find side a and find side b in triangle ABC *Found missing angle by using 180° rule

  23. 6.3 Investigating the Sine Law – Given 2 Angles and any Side and

  24. 6.3 Investigating the Sine Law – Given 2 Angles and any Side

  25. 6.3 Investigating the Sine Law – Given 2 Angles and any Side

  26. Homework • Monday, January 6th - Hwk p.549, #1-4, 6-10, 14 & 15

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