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Tangent lines and inscribed circles a circle is

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Unformatted text preview: city, the higher its average annual temperature. The more annual rainfall a city receives, the lower its average annual temperature. The higher a city’s average annual temperature, the more annual rainfall it receives. The further east a city, the lower its average annual temperature. (E) www.petersons.com 276 Chapter 16 1. RIGHT TRIANGLES AND TRIGONOMETRIC FUNCTIONS Right-triangle trigonometry involves the ratios between sides of right triangles and the angle measures that correspond to these ratios. Refer to the following right triangle, in which the sides opposite angles A, B, and C are labeled a, b, and c, respectively (∠A and ∠B are the two acute angles): Here are the general definitions of the three trigonometric functions sine, cosine, and tangent, and how you would express these three functions in terms of ∠A and ∠B in ∆ABC: a b opposite (sinA = ; sinB = ) c hypotenuse c adjacent b a cosine = (cosA = ; cosB = ) hypotenuse c c opposite a b tangent = (tanA = ; tanB = ) adjacent b a sine = In right triangles with angles 45°-45°-90° and 30°-60°-90°, the values of these trigonometric functions are easily determined. The following figure shows the ratios among the sides of these two uniquely shaped triangles: In a 45°-45°-90° triangle, the lengths of the sides opposite those angles are in the ratio 1 : 1 : 2 , respectively. In a 30°-60°-90° triangle, the lengths of the sides opposite those angles are in the ratio 1 : 3 : 2 , respectively. Accordingly, the sine, cosine, and tangent functions of the 30°, 45°, and 60° angles of any right triangle are as follows: 45°-45°-90° triangle: sin45° = cos45° = tan45° = 1 2 2 30°-60°-90° triangle: sin30° = cos60° = sin60° = cos30° = tan30° = tan60° = 3 3 3 1 2 3 2 www.petersons.com Additional Geometry Topics, Data Analysis, and Probability 277 In SAT problems involving 30°-60°-90° and 45°-45°-90° right triangles, as long as the length of one side is provided, you can use these trigonometric functions to determine the length of any other...
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This note was uploaded on 08/15/2010 for the course MATH a4d4 taught by Professor Colon during the Spring '10 term at Embry-Riddle FL/AZ.

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