1. Warm – up Given the following triangle find the missing side lengths. 1. 2.

2. Trigonometric Ratios Section 5.2- 5.3

3. Standards MM2G2. Students will define and apply sine, cosine, and tangent ratios to right triangles. Discover the relationship of the trigonometric ratios for similar triangles.

4. Essential Question How do I find the sine, the cosine, and the tangent of an acute angle?

5. Vocabulary Trigonometric ratio – a ratio of the lengths of two sides of a right triangle. Three basic trigonometric ratios: Sine (abbreviation: sin) Cosine (abbreviation: cos) Tangent (abbreviation: tan)

6. Trigonometric Ratios Let ∆ABC be a right triangle. The sine, the cosine, and the tangent of the acute angle  A are defined as follows:

7. S O H C A H T O A sin = opp/hyp cos = adj/hyp tan = opp/adj

8. Example 1 Find the sine, the cosine, and the tangent of the indicated angle. Round to 4 decimal places! a.  S b.  R

9. Try This! Find the sine, the cosine, and the tangent of the indicated angle. Round to 4 decimal places! a.  D b.  E

10. Example 2 Find the value of the variable. Round to the nearest tenth.

11. Try This! Find the value of the variable. Round to the nearest tenth.

12. Example 3 Find the value of the variable. Round to the nearest tenth.

13. Try This! Find the value of the variable. Round to the nearest tenth.

14. Vocabulary Angle of Elevation – When you stand and look up at a point in the distance, the angle that your line of sight makes with a line drawn horizontally. Angle of Depression – When you stand at an elevated point and look down at a point in the distance, the angle that your line of sight makes with a line drawn horizontally.

15. Example 4 You are measuring the height of a tree. You stand 45 feet from the base of the tree. You measure the angle of elevation to the top of the tree to be 59 . Find the height of the tree to the nearest tenth of a foot.

16. Summarizer

17. Classwork Worksheet

18. Homework Pages 159 – 160 Number 2 – 20 even Page 166 – 167 Number 2 – 20 even, 26