1. 8.3 Trigonometry SOL: G8 Objectives: The Student Will … Find trigonometric ratios using right Triangles Solve problems using trigonometric ratios

2. Trigonometric Ratios SOH CAH TOA Opposite Sine = Adjacent Cosine = Tangent = Hypotenuse Adjacent Opposite

3. Sine Opposite Hypotenuse Sin A = BC = AC = Opposite Hypotenuse Sin B = AB A C B Hypotenuse

4. Cosine Adjacent Hypotenuse Cos A = Adjacent Hypotenuse Cos B = AB BC = AC = A C B Hypotenuse

5. Tangent Opposite Adjacent Tan B = AC = Opposite Adjacent Tan A = BC = AC BC A C B Hypotenuse

6. Example 1: Find sin L, cos L, tan L, sin N, Cos N, and tan N. Express each ratio as a fraction and as a decimal. Opp Sin L = 8 17 15 == 0.47 Hyp 8 17 Adj Cos L === 0.88 Hyp 15 17 Opp Tan L === 0.53 Adj 8 15 Hypotenuse N M L

7. Example 1: continued Now lets do Sin N, Cos N, and Tan N. Express each ratio as a fraction and as a decimal. Opp Sin N = 8 17 15 == 0.88 Hyp 15 17 Adj Cos N === 0.47 Hyp 8 17 Opp Tan N === 1.88 Adj 15 8 Hypotenuse N M L

8. Study Guide pg 369 Find the indicated trigonometric ratio as a fraction and as a decimal. If necessary, round to the nearest ten- thousandths. 1.) sin A2.) tan B 3.) cos A4.) cos B 5.) sin D6.) tan E 7.) cos E8.) cos D

9. Example 2: Find each value to the nearest ten thousandths. a.) tan 56  = b.) cos 89  = Make sure your calculator is in degree mode 1.4826 0.0175

10. Example 3: Find x. 24° 19 x 1.) 31° 2.) x 34 tan 24° = x 19 (tan 24°)19 =x 8.459345021 = x 8.46 = x cos 31° = x 34 (cos 31°)34 =x 29.14368822 = x 29.14 = x

11. Example 4: A fitness trainer sets the incline on a treadmill to 7 . The walking surface is 5 feet long. Approximately how many inches did the trainer raise the end of the treadmill from the floor? opp sin 7  = 5(sin 7  ) = (5) y5y5 5(sin 7  ) = y Convert to inches y = 12(0.6093467) Hypotenuse Opposite 0.6093467 ft = y ≈ 7.3 y5y5 = hyp

12. Using Trigonometry to Find the Angle Measure We can also find an angle measure. If sin B = 0.7823, then sin -1 (0.7823) = B This is done in the calculator: Press the 2 nd key, press the sin (sin -1 ) key Type in 0.7823 and press enter B = 51.47 

13. Examples 5: Find the measure of each acute angle to the nearest tenth degree. a.) tan A = 0.2356, b.) cos R = 0.6401, A = 13.3 tan -1 (0.2356) = A cos -1 (0.6401) = R R = 50.2

14. Example 6: Find x. 18 15 x°x° tan x° = 15 18 x°x° 39.80557109° = x 39.81° = tan -1 ( ) = 15 18

15. Example 7: Find x. 17 12 x°x° sin x° = 12 17 (sin x°)17 = 12 44.90087216° = x (sin x°)17 =12 17 (sin x°) = 12 17 ( sin -1 ) = x 12 17 44.9° =

16. Study Guide pg 370 Find x. Round to the nearest tenth.

17. Study Guide pg 370 Find x. Round to the nearest tenth.