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8-2 8-2 Trigonometric TrigonometricRatios Ratios Warm Up Lesson Presentation Lesson Quiz Holt Geometry Holt Geometry 8-2 Trigonometric Ratios Warm Up Write each fraction as a decimal rounded to the nearest hundredth. 1. 2. 0.67 0.29 Solve each equation. 3. Holt Geometry x = 7.25 4. x = 7.99 8-2 Trigonometric Ratios Objectives Find the tangent of an acute angle. Use trigonometric ratios to find side lengths and angles in right triangles. Holt Geometry 8-2 Trigonometric Ratios Vocabulary trigonometric ratio tangent Holt Geometry 8-2 Trigonometric Ratios By the AA Similarity Postulate, a right triangle with a given acute angle is similar to every other right triangle with that same acute angle measure. So ∆ABC ~ ∆DEF ~ ∆XYZ, and . These are trigonometric ratios. A trigonometric ratio is a ratio of two sides of a right triangle. Holt Geometry 8-2 Trigonometric Ratios Note 66 Holt 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 tangent of A is written as tan A. Holt Geometry 8-2 Trigonometric Ratios Example 1A: Finding Trigonometric Ratios Write the trigonometric ratio as a fraction and as a decimal rounded to the nearest hundredth. tan J Holt Geometry 8-2 Trigonometric Ratios Example 1B: Finding Trigonometric Ratios Write the trigonometric ratio as a fraction and as a decimal rounded to the nearest hundredth. Tan K Holt Geometry 8-2 Trigonometric Ratios Example 2: Finding Trigonometric Ratios in Special Right Triangles Use a special right triangle to write tan 30° as a fraction. Holt Geometry 8-2 Trigonometric Ratios Check It Out! Example 2 Use a special right triangle to write tan 45° as a fraction. 45° s 45° s Holt Geometry 8-2 Trigonometric Ratios Example 3C: Calculating Trigonometric Ratios Use your calculator to find the trigonometric ratio. Round to the nearest hundredth. tan 65° Caution! Be sure your calculator is in degree mode, not radian mode. tan 65° 2.14 Holt Geometry 8-2 Trigonometric Ratios Check It Out! Example 3a Use your calculator to find the trigonometric ratio. Round to the nearest hundredth. tan 11° tan 11° 0.19 Holt Geometry 8-2 Trigonometric Ratios Example 4A: Using Trigonometric Ratios to Find Lengths Find the length. Round to the nearest hundredth. BC Holt 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 Geometry 8-2 Trigonometric Ratios Example 4C: Using Trigonometric Ratios to Find Lengths Find the length and the missing angle. Round to the nearest hundredth. ED D Holt Geometry 8-2 Trigonometric Ratios Check It Out! Example 4c Find the length and the missing angle. Round to the nearest hundredth. BC A Holt Geometry 8-2 Trigonometric Ratios Exit Slip Use a special right triangle to write each trigonometric ratio as a fraction. 1. tan 60° 2. tan 45° Use your calculator to find each trigonometric ratio. Round to the nearest hundredth. 3. tan 84° Find each length. Round to the nearest tenth. 4. CB Holt Geometry