1. WARM UP Find the following missing values. Find the following missing values. 1)2)

2. Section 8.6 Sine and Cosine Ratios

3. Three Trig. Ratios 1) sine 2) cosine 3) tangent Today we are looking at the Sine and Cosine Sine and Cosine

4. sine ratio A B C Leg opposite Hypotenuse

5. cosine ratios A B C Leg adjacent Hypotenuse

6. X Y b 1. Find cos X 2. Find sin X 3. Find cos Y 4. Find sin Y We must first find “b”.It’s a Pythagorean Triple! So b = 12 b = 12

7. Calculator Stuff MAKE SURE YOU ARE IN DEGREE MODE EVERY TIME!!!!!!!!!!!!!!

8. Calculator Stuff Find the missing values. 5) sin 34 o = 6) cos 89 o = 7) sin ? o = 0.1510 8) cos ? o =.5592 0.5591929 0.0174524 Use sin -1 on calc8.68488 o Use cos -1 on calc 55.9995 o

9. o 9) Find the measure of the missing angles and lengths. z = 180 – 90 – 28 = 62 o 62 o 469 You can use TRIG or PYTHA. THM to find “y” 883

10. HINT: It is easiest to find the missing value that has two known values…….. In this case find “z” first since you already know two sides. Find the missing values. 10) 24 37 o 180- 90 – 37 = 53 o

11. Drop the Altitude from the vertex angle B and make two right triangles. Now you can use trig to find the missing angles. Find the measures of all three angles. This is a great problem! Can be very tricky!!! 22 66 o 180 – 66 – 66 = 48 o 48 o

12. LADDERS ! 12) A 6 m ladder reaches higher up a wall when placed at a 70 degree angle than when placed at a 60 degree angle. How much higher, to the nearest tenth of a meter?

13. LADDERS ! 12) A 6 m ladder reaches higher up a wall when placed at a 70 degree angle than when placed at a 60 degree angle. How much higher, to the nearest tenth of a meter? 70 o 60 o 6 feet 70 o 6 feet

14. LADDERS ! 12) A 6 m ladder reaches higher up a wall when placed at a 70 degree angle than when placed at a 60 degree angle. How much higher, to the nearest tenth of a meter? 70 o 60 o 6 feet 70 o 6 feet x y 5.6382 – 5.196 = 0.4422 = 0.4 ft

15. PRACTICE Page 313 - 314 Page 313 - 314 Classroom Exercises Classroom Exercises #1 – 13 #1 – 13