1. How to use sine, cosine, and tangent ratios to determine side lengths in triangles. Chapter 8.3-8.4GeometryStandard/Goal: 2.2, 4.1

2. 1. Check and discuss assignment from yesterday. 2. Work on Quiz 8.2 3. Read, write, and discuss how to use sine, cosine, and tangent ratios to determine side lengths in triangles. 4. Work on given assignment.

3. Trigonometric ratio: a ratio of the lengths of two sides of a right triangle. Trigonometry meaning measurement of triangles. The three basic trigonometric ratios are: sine ( sin ) cosine ( cos ) tangent ( tan )

4. Let Δ ABC be a right triangle. The sine, the cosine, and the tangent of the acute are defined as follows. b ca B C A side opposite side adjacent hypotenuse

5. SOHCAHTOA or Some Old Horse Caught Another Horse Taking Oats Away

6. tan A 20 21 === opposite adjacent BC AC tan B 21 20 === opposite adjacent AC BC Write the tangent ratios for A and B. Lesson 8-3

7. Use the triangle to find the ratios of sin T, cos T, sin G, and cos G. Write your answer in simplest terms. Lesson 8-4 sin T == 12 20 3535 = opposite hypotenuse cos T == 16 20 4545 = adjacent hypotenuse sin G == 16 20 4545 = opposite hypotenuse cos G == 12 20 3535 = adjacent hypotenuse

9. To measure the height of a tree, Alma walked 125 ft from the tree and measured a 32° angle from the ground to the top of the tree. Estimate the height of the tree. The tree forms a right angle with the ground, so you can use the tangent ratio to estimate the height of the tree. tan 32° = height 125 Use the tangent ratio. height = 125 (tan 32°)Solve for height. 125 32 78.108669 Use a calculator. The tree is about 78 ft tall. Lesson 8-3

10. A 20-ft. wire supporting a flagpole forms a 35˚ angle with the flagpole. To the nearest foot, how high is the flagpole? The flagpole, wire, and ground form a right triangle with the wire as the hypotenuse. Because you know an angle and the measures of its adjacent side and the hypotenuse, you can use the cosine ratio to find the height of the flagpole. Lesson 8-4 cos 35° = height 20 Use the cosine ratio. height = 20 cos 35°Solve for height. 20 35 16.383041 Use a calculator. The flagpole is about 16 ft tall.

12. Find m R to the nearest degree. tan R = 47 41 Find the tangent ratio. So m R 49. Lesson 8-3 m R tan –1 Use the inverse of the tangent. 47 41 Use a calculator. 48.900494 47 41

13. A right triangle has a leg 1.5 units long and hypotenuse 4.0 units long. Find the measures of its acute angles to the nearest degree. Draw a diagram using the information given. Use the inverse of the cosine function to find m A. cos A = 1.5 4.0 0.375=Use the cosine ratio. Use the inverse of the cosine. m A = cos –1 (0.375) Use a calculator. 0.375 67.975687 Round to the nearest degree. m A 68 Lesson 8-4 Additional Examples

14. (continued) To find m B, use the fact that the acute angles of a right triangle are complementary. The acute angles, rounded to the nearest degree, measure 68 and 22. m A + m B = 90Definition of complementary angles Substitute.68 + m B 90 m B 22 Lesson 8-4

15. Kennedy, D., Charles, R., Hall, B., Bass, L., Johnson, A. (2009) Geometry Prentice Hall Mathematics. Power Point made by: Robert Orloski Jerome High School.