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 A C B 29.5cm 44° 37.1cm Ex. 1 Find angle C

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

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

13. Humour Break

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

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. 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 A C B b 72° 43° 27.2cm a Ex. 3 Find the length side a and side 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

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