2. How would you solve the right triangles: 1)2) 12 x 1663° x y 14 28°

3. Section 9.5 Saturday, June 11, 2016 Trig Ratios Standards #18&19

4. Trig Ratios (Soh/Cah/Toa) ∆ABC is a right triangle. The sine, the cosine, and the tangent of the acute angle, ∡ A, are defined as follows: SinA = opposite/hypotenuse = a/c CosA = adjacent/hypotenuse = b/c TanA = opposite/adjacent = a/b (Hypotenuse) c b (Side adjacent to ∡ A) (next to) a (side opp. ∡ A) AC B

5. Trig Ratios (Soh/Cah/Toa) ∆ABC is a right triangle. The sine, the cosine, and the tangent of the acute angle, ∡ B, are defined as follows: SinB = opposite/hypotenuse = b/c CosB = adjacent/hypotenuse = a/c TanB = opposite/adjacent = b/a (Hypotenuse) c b (Side opposite to ∡ B) a (side adj. ∡ B) AC B

6. Example 1 Use the TRIG ratio sheet to approximate the sine, cosine, and tangent of 82° to 3 decimal places.

7. Answers to #1 sin 82° =.990 cos 82° =.139 tan 82° = 7.115

8. Example 2 11 19 15 Use the diagram to find the trig ratios of the 2 acute angles: Sin D, Cos D, Tan D and the Sin E, Cos E and Tan E. E F D

9. Answers to #2 (Soh/Cah/Toa) sin = opp/hyp, cos = adj./hyp, tan = opp/adj. ∠ D: sin D = 11 cos D = 15 tan D = 11 19 19 19 ∠ E: sin E = 15 cos E = 11 tan D = 15 19 19 11

10. Example 3 t u 8 Find the 3 missing parts of the following right triangle. Round decimals to the nearest 10 th. 65 ∘ w T U V

11. Answers to #3 1)First thing to do is to find the 3 rd angle, w : 90°-65° = 25° 2) Then pick one of the sides to solve for first, it does NOT matter which side you pick. Use TRIG to find that side and then use TRIG or the Pythagorean Theorem to find the 3 rd side. Make sure to round ALL answers to the nearest 10 th. u: 1) cos = a/ht: 1) sin = o/h 2) c = u/8 2) s = t/8 3) cos65 = u 3) sin65 = t 8 8 4) u = 8(cos65) 4) t = 8(sin65) 5) u = 8(.4226) 5) t = 8(.9063) 6) u ≈ 3.38 ≈ 3.4 6) t ≈ 7.25 ≈ 7.3

12. Answer to #3 cont… 1)If you solved for u first, you could have used the Pythagorean Theorem to find t: 3.4 2 + t 2 = 8 2  11.6 + t 2 = 64  t 2 = 64 – 11.6  t 2 = 52.4  t ≈ 7.2 2) Conversely, if you solved for t first, you could have used the Pythagorean Theorem to find u: 7.3 2 + u 2 = 8 2  53.3 + u 2 = 64  u 2 = 64 – 53.3  u 2 = 10.7  u ≈ 3.3

13. Example 4 w 17 38 ∘ z Find the value of each variable. Use TRIG to find both missing sides. Round decimals to nearest 10 th. x

14. Answers to #4 1) 90° - 38° = 52° (missing 3 rd angle, x) 2) w: 1) tan = o/az: 1) cos = a/h 2) t = w 2) c = 17 17 z 3) tan38 = w 3) cos38 = 17 17z 4) w = 17(tan38) 4) z = 17/cos38 5) w = 17(.7813) 5) z = 17/.7880 6) w ≈ 13.28 ≈ 13.3 6) z = 21.57 ≈ 21.6 Again, once you have found the 2 nd side if you would like to use Pythagorean Theorem to find the 3 rd side you can. Just make sure that you round to the nearest 10 th.

15. Example 5 Vocabulary: The angle that your line of sight makes with a line drawn horizontally is called the angle of elevation. You are measuring the height of a building. You stand 100 feet from the base of the building. You measure the angle of elevation from a point on the ground to the top of the building to be 48°. Estimate the height of the building.

16. Answer to #5 100 ft. 48° X 1)t = o/a 2)tan48 = x 100 3) x = 100(tan48) 4) x = 100(1.1106) 5) x ≈ 111.06 ≈ 111.1 ft

17. Assignment Day #1 (Geo 10-12) 9.5 P.562 #3-8(together),10,11 16-27 Draw pictures… Show work… Write Soh/Cah/Toa…

18. Assignment Day #2 (Geo 10-12) 9.5 P.562 #12,13,28-33,37,38 Draw pictures… Show work… Write Soh/Cah/Toa…

19. Assignment Day #1 (Geo 9) 9.5 P.562 #10,11,16-27 Draw pictures… Show work… Write Soh/Cah/Toa…

20. Assignment Day #2 (Geo 9) 9.5 P.562 #3-8,28-33,37,38 Draw pictures… Show work… Write Soh/Cah/Toa…