1 / 25

Mastering Right Triangle Trigonometry: Functions and Calculations

Dive into the essentials of right triangle trigonometry. This guide covers the calculation of trigonometric functions for acute angles, including sine, cosine, tangent, and their reciprocals. Learn how to solve for unknown triangle measures using ratios and inverse functions. With clear step-by-step examples, including detailed assignments and practice problems, you'll master finding exact answers as fractions and rounding to the nearest ten-thousandth. Whether you're tackling homework or preparing for a quiz, this resource will effectively enhance your understanding and skills in trigonometry.

price-bates
Télécharger la présentation

Mastering Right Triangle Trigonometry: Functions and Calculations

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related