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D.N.A. Find the missing sides of the special right triangles. 1) 7 3 2) 30 45 12 45 3) Solve for x. 19 x 60 11 Complete your DNA on a fresh sheet of paper. Label it as shown on the board. Chapter 8-4 Trigonometry • trigonometry • Find trigonometric ratios using right triangles. • Solve problems using trigonometric ratios. • trigonometric ratio • sine • cosine • tangent Standards 18.0 Students know the definitions of the basic trigonometric functions defined by the angles of a right triangle. They also know and are able to use elementary relationships between them. For example, tan(x) = sin(x)/cos(x), (sin(x))2 + (cos(x))2 = 1. (Key) Standards 19.0 Students use trigonometric functions to solve for an unknown length of a side of a right triangle, given an angle and a length of a side. (Key) The Amazing Legend of… Chief SohCahToa Chief SohCahToa • Once upon a time there was a wise old Native American Chief named Chief SohCahToa. • He was named that due to an chance encounter with his coffee table in the middle of the night. • He woke up hungry, got up and headed to the kitchen to get a snack. • He did not turn on the light and in the darkness, stubbed his big toe on his coffee table…. opposite side Sine(Sin) S o:h hypotenuse adjacent side Cosine(Cos ) C a:h hypotenuse opposite side Tangent(Ta n) B adjacent side T o:a Opposite Side A Adjacent Side C Find Sine, Cosine, and Tangent Ratios Find sin L, cos L, tan L, sin N, cos N, and tan N. Express each ratio as a fraction and as a decimal. S o : h C a : h L 8 : 17 15 : 17 Hypotenuse 15 8 17 17 Adjacent To:a 8 : 15 8 15 Find Sine, Cosine, and Tangent Ratios Find sin L, cos L, tan L, sin N, cos N, and tan N. Express each ratio as a fraction and as a decimal. Ca :h N Hypotenuse Adjacent S o :h 15 : 17 15 17 8 : 17 8 17 T o:a 15 : 8 15 8 Find Sine, Cosine, and Tangent Ratios Answer: A. Find sin A. A. B. C. D. 0% 0% A B A. A B. 0% B C. C C D. D 0% D B. Find cos A. A. B. C. D. 0% 0% A B A. A B. 0% B C. C C D. D 0% D C. Find tan A. A. B. C. D. 0% 0% A B A. A B. 0% B C. C C D. D 0% D D. Find sin B. A. B. C. D. 0% 0% A B A. A B. 0% B C. C C D. D 0% D E. Find cos B. A. B. C. D. 0% 0% A B A. A B. 0% B C. C C D. D 0% D F. Find tan B. A. B. C. D. 0% 0% A B A. A B. 0% B C. C C D. D 0% D Using a Trig. Table Find the Sine Cosine and Tangent of Find the Sine Cosine and Tangent of Find the Sine Cosine and Tangent of Find the Sine Cosine and Tangent of Angle Measure 10 26 Sin Cos Tan Angle Measure Sin Cos 10 56 26 72 Tan .1736 .9848 .1763 56 .8290 .5592 1.483 .4877 72 .9511 .3090 3.077 .4384 .8988 A. Use your trig. table to find sin 48° to the nearest ten thousandth. A. 0.6691 B. 1.1106 C. 0.7431 D. 0.7314 0% 1. 2. 3. 4. A B C D A B C D B. Use your trig. table to find cos 85° to the nearest ten thousandth. A. 0.0872 B. 0.9962 C. 11.4301 D. 0.0698 0% 1. 2. 3. 4. A B C D A B C D Use Trigonometric Ratios to Find a Length EXERCISING A fitness trainer sets the incline on a treadmill to 7°. The walking surface is 5 feet long. Approximately how many inches did the trainer raise the end of the treadmill from the floor? =60 in Let y be the height of the treadmill from the floor in inches. The length of the treadmill is 5 feet, or 60 inches. opposite sin 7 hypotenuse y .1219 60 y 60(.1219) 60 60 y =7.314 in Answer: The treadmill is about 7.3 inches high. CONSTRUCTION The bottom of a handicap ramp is 15 feet from the entrance of a building. If the angle of the ramp is about 4.8°, how high does the ramp rise off the ground to the nearest inch? A. 1 in. B. 11 in. C. 16 in. 1. 2. 3. 4. D. 15 in. 0% A B C D A B C D Use Trigonometric Ratios to Find an Angle Measure COORDINATE GEOMETRY Find mX in right ΔXYZ for X(–2, 8), Y(–6, 4), and Z(–3, 1). XY 4 2 4 2 32 4 2 4 2 XZ 7 1 50 5 2 2 5 2 3 2 2 YZ 32 32 18 3 2 Use Trigonometric Ratios to Find an Angle Measure COORDINATE GEOMETRY Find mX in right ΔXYZ for X(–2, 8), Y(–6, 4), and Z(–3, 1). XY 4 2 5.656 5.46562 37 57.071 2 3 243 2 4. XZ 5 2 7.071 YZ 3 2 4.243 Opposite 4.243 SinX 0.6 Hypotenuse 7.071 mX 37 from trig. table COORDINATE GEOMETRY Find mA in right ΔABC to the nearest degree. A. 66.0° B. 56.3° C. 33.7° D. 24.0° A. B. C. D. A B C D Homework Chapter 8-4 • Pg 460: # 1, 2, 10, 11, 14 – 17 all, 26, 29 – 49 odd