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Right-Angle Right-AngleTrigonometry Trigonometry • How do we understand and use trigonometric relationships of acute angles in triangles? • How do we determine side lengths of right triangles by using trigonometric functions? HoltMcDougal Algebra 2Algebra 2 Holt Right-Angle Trigonometry A trigonometric function is a function whose rule is given by a trigonometric ratio. A trigonometric ratio compares the lengths of two sides of a right triangle. The Greek letter theta θ is traditionally used to represent the measure of an acute angle in a right triangle. The values of trigonometric ratios depend upon θ. Holt McDougal Algebra 2 Right-Angle Trigonometry Holt McDougal Algebra 2 Right-Angle Trigonometry Finding Trigonometric Ratios 1. Find the value of the opp. sine, cosine, and tangent functions for θ. hyp. adj. sin θ = cos θ = tan θ = Holt McDougal Algebra 2 Right-Angle Trigonometry Finding Trigonometric Ratios 2. Find the value of the adj. sine, cosine, and tangent functions for θ. hyp. opp. sin θ = cos θ = tan θ = Holt McDougal Algebra 2 Right-Angle Trigonometry You will frequently need to determine the value of trigonometric ratios for 30°,60°, and 45° angles as you solve trigonometry problems. Recall from geometry that in a 30°-60°-90° triangle, the ration of the side lengths is 1: 3 :2, and that in a 45°-45°-90° triangle, the ratio of the side lengths is 1:1: 2. Holt McDougal Algebra 2 Right-Angle Trigonometry Holt McDougal Algebra 2 Right-Angle Trigonometry Finding Side Lengths of Special Right Triangles 3. Use a trigonometric function to find the value of x. Which function relates the opposite and the hypotenuse? ° Substitute 30° for θ, x for opp, and 74 for hyp. Substitute 2x = 74 x = 37 Holt McDougal Algebra 2 hyp. Solve for x. for sin 30°. opp. Right-Angle Trigonometry Finding Side Lengths of Special Right Triangles 4. Use a trigonometric function to find the value of x. Which function relates the opposite and the hypotenuse? ° Substitute 45° for θ, x for opp, and 20 for hyp. Substitute 2 x 20 2 Holt McDougal Algebra 2 Solve for x. for sin 45°. hyp. opp. Right-Angle Trigonometry Caution! Make sure that your calculator is set to interpret angle values as degrees. Press DRG. Check that Degree and not Radian is highlighted. Holt McDougal Algebra 2 Right-Angle Trigonometry Finding Side Lengths of Other Right Triangles 5. Use a trigonometric function to find the value of x. 42 tan 38 x 42 x o tan 38 o x 53.76 Holt McDougal Algebra 2 Which function relates the opposite and the adjacent? Substitute 38 for θ, 42 for opp., and x for adj. 42 opp. Because x is on bottom, divide. 38 o x adj. Right-Angle Trigonometry Finding Side Lengths of Other Right Triangles 6. Use a trigonometric function to find the value of x. adj cos hyp Which function o 52 x relates the adjacent and the hypotenuse? adj. x cos 52 155 Substitute 52 for θ, x for adj., and 155 for hyp. x 155 cos 52 Because x is on top, multiply. o x 95.43 Holt McDougal Algebra 2 o hyp. 155 Right-Angle Trigonometry Lesson 10.1 Practice A Holt McDougal Algebra 2