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Do Now

Do Now. Rewrite as a decimal to nearest ten thousandth place (4 decimal places). 13/24 24/13 Solve 0.3 = m/8 1.25 = 7/y Find the unknown value in a right Δ if the hypotenuse is 6.9 and one leg is 3.5. Right-Triangle Trigonometry. Section 13.1. Essential Question.

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Do Now

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  1. Do Now Rewrite as a decimal to nearest ten thousandth place (4 decimal places). • 13/24 • 24/13 Solve • 0.3 = m/8 • 1.25 = 7/y • 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 • 8/17, 0.4706 • 15/17, 0.8824 • 8/17, 0.4706 • 15/17, 0.8824 • 8/15, 0.5333 • 15/8, 1.8750 • 17/15, 1.1333 • 17/8, 2.1250 • 17/15, 1.1333 17. 17/8, 2.1250 • 8/15, 0.5333 • 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 • Solve ∆ PQR. Find the measurement of <Q to the nearest degree and RP and RQ to the nearest tenth. • 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 • Solve ∆ ABC. Find the measurement of <A to the nearest degree and AC and BC to the nearest tenth. • 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 • 36° • 30° • 48° • 21° • 49° • 41° • < A = 39°, < B = 51° AB = 6.4 • < R = 32°, < S = 58 ST = 2.1 • < A = 40°, AB = 9.5 AC = 7.3 • < S = 50°, RS = 11.4 RT = 8.7 42. < B = 55°, AC=10.2 BC = 7.2 • < B = 48°, BC = 3.8 AC = 4.2

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

  21. Pg. 982, 13.1 #’s 1-18 • 20/29, 0.6897 • 21/29, 0.7241 • 21/29, 0.7241 • 20/29, 0.6897 • 20/21, 0.9524 • 21/20, 1.05 • 29/20, 1.45 • 29/21, 1.3810 • 29/21, 1.3810 • 29/20, 1.45 • 21/20, 1.05 • 20/21, 0.9524 • <G=53°, GI=2.6, GH=4.4 • <E=52°, <D=38°, EF=4.3 • <J=56°, <K=34°, JK=14.4 • <A=27°, <B=63°, AB=6.7

  22. Continued… 17. <M=64°, MN=22.1, NO=19.9 18. <R=32°, SQ=8.1, QR=13.0 Workbook pg.82,13.1 • 40/41, 0.9756 • 9/41, 0.2195 • 40/9, 4.4444 • 9/41, 0.2195 • 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°

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

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