Holt McDougal Algebra 2 Right-Angle Trigonometry Holt Algebra 2Holt McDougal Algebra 2 How do we understand and use trigonometric relationships of acute.

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Presentation transcript:

Holt McDougal Algebra 2 Right-Angle Trigonometry Holt Algebra 2Holt McDougal Algebra 2 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?

Holt McDougal Algebra 2 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 sine, cosine, and tangent functions for θ. sin θ = cos θ = tan θ = opp. hyp. adj.

Holt McDougal Algebra 2 Right-Angle Trigonometry Finding Trigonometric Ratios 2.Find the value of the sine, cosine, and tangent functions for θ. sin θ = cos θ = tan θ = opp. hyp. adj.

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. ° 2x = 74 Which function relates the opposite and the hypotenuse? Solve for x. Substitute for sin 30°. Substitute 30° for θ, x for opp, and 74 for hyp. opp. hyp. x = 37

Holt McDougal Algebra 2 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? opp. hyp. Substitute 45 for θ, x for opp, and 20 for hyp. ° ° Substitute for sin 45°. Solve for x.

Holt McDougal Algebra 2 Right-Angle Trigonometry Make sure that your calculator is set to interpret angle values as degrees. Press DRG. Check that Degree and not Radian is highlighted. Caution!

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. opp. adj. Because x is on bottom, divide. Substitute 38 for θ, 42 for opp., and x for adj. Which function relates the opposite and the adjacent?

Holt McDougal Algebra 2 Right-Angle Trigonometry Finding Side Lengths of Other Right Triangles 6.Use a trigonometric function to find the value of x. hyp. adj. Because x is on top, multiply. Substitute 52 for θ, x for adj., and 155 for hyp. Which function relates the adjacent and the hypotenuse?

Holt McDougal Algebra 2 Right-Angle Trigonometry Lesson 10.1 Practice A