Unit 6 Lesson 6b Trigonometric Ratios CCSS G-SRT 6: Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles. G-SRT 7: Explain and use the relationship between the sine and cosine of complementary angles. G-SRT 8: Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. Lesson Goals Use Trigonometric Ratios to find missing side lengths in triangles. ESLRs: Becoming Effective Communicators, Competent Learners and Complex Thinkers

Using Trigonometric Ratios Trigonometric Ratios can be used to find missing side lengths. 1.Determine which trig ratio to use (sin, cos, tan). 2.Write an equation with the given values 3.Find the value of the ratio on a trigonometric chart or scientific calculator. 4.Solve the equation.

Example 34 o 13 x

34 o 13 x Example

51 o 20 x

You Try 40 o 10 x

You Try 70 o 5 x

You Try 50 o 9 x

Example 60 o 8 m h 12 m

Definition Angle of Elevation The angle created when looking at something high and a horizontal line.

Definition Angle of Depression The angle created when looking at something low and a horizontal line.

Example While visiting the Pigeon Point Lighthouse, you wonder how tall the lighthouse is. Standing 100 feet from the base of the lighthouse, you discover that the angle of elevation is 49 o. Use a trigonometric ratio to find the height. 100 ft 49 o h

Summary SOHCAHTOA is one way to remember the three basic trigonometric ratios. How will you remember the correct ratio for sine, cosine, and tangent? What is a trigonometric identity? How are trigonometric ratios used?

p. 563: 28 – 38 e, 41, 49, 51