1. Do Now Rewrite as a decimal to nearest ten thousandth place (4 decimal places). 1.13/24 2.24/13 Solve 3.0.3 = m/8 4.1.25 = 7/y 5.Find the unknown value in a right Δ if the hypotenuse is 6.9 and one leg is 3.5.

2. Right-Triangle Trigonometry Section 13.1

3. Essential Question How do I find the trigonometry functions of acute angles and solve a right triangle using trigonometry functions?

4. SOH CAH TOA

5. Example 1 Find the values of the 6 trig functions of < X for Δ XYZ. Give exact answers (fractions) and answers rounded to the nearest ten- thousandth (four decimal places).

6. Example 2 Find the values of the 6 trig functions of < L for ∆ KLM. Give exact answers and answers rounded to the nearest ten thousandth place (four decimal places).

7. Assignment Pg. 833, 8-31 all

8. Pg. 833 8-31 all 8.8/17, 0.4706 9.15/17, 0.8824 10. 8/17, 0.4706 11. 15/17, 0.8824 12. 8/15, 0.5333 13. 15/8, 1.8750 14. 17/15, 1.1333 15. 17/8, 2.1250 16. 17/15, 1.1333 17. 17/8, 2.1250 18. 8/15, 0.5333 19. 15/8, 1.8750 20-31 on next slide

9. #’s 20-31

10. Do Now: Find all six trig functions for < Z. Give exact answers (reduced fractions) and answers rounded to the nearest ten-thousandths. SIN= CSC= COS= SEC= TAN= COT=

11. Finding angle measures To find the measurement of an angle in a right triangle using only the lengths of two sides, you must use the inverse of the appropriate trig function. ***Your graphing calculator must be set to “degrees” in the “mode” function.

12. Example 3 Solve ∆ RST. Give m < R and m < S to the nearest degree, and give RT to the nearest tenth:

13. Example 4 For ∆ ABC find each side length to the nearest tenth and the measurement of < B:

14. Example 5 For ∆ RST, find each side length to the nearest tenth and any missing angle measure:

15. Example 6 Find the length BE in the figure below:

16. Assignment Pg. 833-834, 32-43 all

17. Do Now 1.Solve ∆ PQR. Find the measurement of <Q to the nearest degree and RP and RQ to the nearest tenth. 2.Find the values for the six trig functions for <X for ∆ XYZ. Give exact answers and answers rounded to the nearest ten- thousandth.

18. Do Now 1.Solve ∆ ABC. Find the measurement of <A to the nearest degree and AC and BC to the nearest tenth. 2.Find the values for the six trig functions for <Z for ∆ XYZ. Give exact answers and answers rounded to the nearest ten- thousandth.

19. Pg. 833-834, 32-43 all 32. 36° 33. 30° 34. 48° 35. 21° 36. 49° 37. 41° 38. < A = 39°, < B = 51° AB = 6.4 39.< R = 32°, < S = 58 ST = 2.1 40.< A = 40°, AB = 9.5 AC = 7.3 41.< S = 50°, RS = 11.4 RT = 8.7 42. < B = 55°, AC=10.2 BC = 7.2 43.< B = 48°, BC = 3.8 AC = 4.2

21. QUIZ TOMORROW OVER 13.1!! Today’s Assignment: pg. 982 13.1, 13-18 all Worksheet 13.1, 1-15 all

22. Pg. 982, 13.1 #’s 1-18 1.20/29, 0.6897 2.21/29, 0.7241 3.21/29, 0.7241 4.20/29, 0.6897 5.20/21, 0.9524 6.21/20, 1.05 7.29/20, 1.45 8.29/21, 1.3810 9.29/21, 1.3810 10.29/20, 1.45 11. 21/20, 1.05 12. 20/21, 0.9524 13.<G=53°, GI=2.6, GH=4.4 14. <E=52°, <D=38°, EF=4.3 15. <J=56°, <K=34°, JK=14.4 16. <A=27°, <B=63°, AB=6.7

23. Continued… 17. <M=64°, MN=22.1, NO=19.9 18. <R=32°, SQ=8.1, QR=13.0 Workbook pg.82,13.1 1.40/41, 0.9756 2.9/41, 0.2195 3.40/9, 4.4444 4.9/41, 0.2195 5.40/41, 0.9756 6. 9/40, 0.225 7. 41/9, 4.5556 8. 41/9, 4.5556 9. 40/9, 4.4444 10. XZ=8.3, <X=57°, <Z=33° 11. UV=11.6, <U=61°, <W=29° 12. RT=21.6, <R=34°, <T=56°

24. Continued… 13. <Q=59°, QN=4.9, NP=4.2 14. <L=36°, LM=4.9, MN=3.5 15. <J=56°, HJ=5.2, HK=4.3