8 2 Trigonometric Ratios Objectives Find the sine

8 -2 Trigonometric Ratios Objectives Find the sine, cosine, and tangent of an acute angle. Use trigonometric ratios to find side lengths in right triangles and to solve real-world problems. Holt Mc. Dougal Geometry

8 -2 Trigonometric Ratios Vocabulary trigonometric ratio sine cosine tangent Holt Mc. Dougal Geometry

8 -2 Trigonometric Ratios _________– a ratio of two sides of a right triangle. Holt Mc. Dougal Geometry

8 -2 Trigonometric Ratios Holt Mc. Dougal Geometry

8 -2 Trigonometric Ratios Writing Math In trigonometry, the letter of the vertex of the angle is often used to represent the measure of that angle. For example, the sine of A is written as sin A. Holt Mc. Dougal Geometry

8 -2 Trigonometric Ratios Example 1 A: Finding Trigonometric Ratios Write the trigonometric ratio as a fraction and as a decimal rounded to the nearest hundredth. sin J cos J tan K Holt Mc. Dougal Geometry

8 -2 Trigonometric Ratios Example 1 b Write the trigonometric ratio as a fraction and as a decimal rounded to the nearest hundredth. cos A tan B sin B Holt Mc. Dougal Geometry

8 -2 Trigonometric Ratios Example 2 a Use a special right triangle to write cos 30° as a fraction. Draw and label a 30º-60º-90º ∆. Holt Mc. Dougal Geometry

8 -2 Trigonometric Ratios Example 2 b Use a special right triangle to write tan 45° as a fraction. Draw and label a 45º-90º ∆. Holt Mc. Dougal Geometry

8 -2 Trigonometric Ratios Example 3 A: Calculating Trigonometric Ratios Use your calculator to find the trigonometric ratio. Round to the nearest hundredth. sin 52° Caution! Be sure your calculator is in degree mode, not radian mode. Holt Mc. Dougal Geometry

8 -2 Trigonometric Ratios Example 3 Continued Use your calculator to find the trigonometric ratio. Round to the nearest hundredth. 3 b. cos 19° Holt Mc. Dougal Geometry 3 c. tan 65° 3 d. sin 62°

8 -2 Trigonometric Ratios Example 4 A: Using Trigonometric Ratios to Find Lengths Find the length. Round to the nearest hundredth. BC Holt Mc. Dougal Geometry

8 -2 Trigonometric Ratios Caution! Do not round until the final step of your answer. Use the values of the trigonometric ratios provided by your calculator. Holt Mc. Dougal Geometry

8 -2 Trigonometric Ratios Example 4 B: Using Trigonometric Ratios to Find Lengths Find the length. Round to the nearest hundredth. QR Holt Mc. Dougal Geometry

8 -2 Trigonometric Ratios Example 4 C: Using Trigonometric Ratios to Find Lengths Find the length. Round to the nearest hundredth. FD Holt Mc. Dougal Geometry

8 -2 Trigonometric Ratios Example 4 d Find the length. Round to the nearest hundredth. JL Holt Mc. Dougal Geometry

8 -2 Trigonometric Ratios Example 5 a: Problem-Solving Application The Pilatusbahn in Switzerland is the world’s steepest cog railway. Its steepest section makes an angle of about 25. 6º with the horizontal and rises about 0. 9 km. To the nearest hundredth of a kilometer, how long is this section of the railway track? Holt Mc. Dougal Geometry

8 -2 Trigonometric Ratios Example 5 a Continued 1 Understand the Problem Make a sketch. 0. 9 km Holt Mc. Dougal Geometry

8 -2 Trigonometric Ratios Example 5 a Continued 2 Make a Plan 3 Solve Holt Mc. Dougal Geometry

8 -2 Trigonometric Ratios Example 5 b Find AC, the length of the ramp, to the nearest hundredth of a foot. Holt Mc. Dougal Geometry

8 -2 Trigonometric Ratios Example 5 b Continued 1 Understand the Problem 2 Make a Plan Holt Mc. Dougal Geometry

8 -2 Trigonometric Ratios Example 5 b Continued 3 Solve Holt Mc. Dougal Geometry