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Trigonometry Trigonometry is the study of the relationships between the sides and angles of triangles. More specifically, right triangles. Trigonometry has its origins in astronomy (i.e. measuring the distance to the moon). These ratios were discovered by the mathematician Hipparchus and the astronomer Ptolemy. 1. Are these three triangle similar? How do you know (what post/theorem)? 2. What do you observe about angle A, angle B, and angle C? 3. Use the above right triangles to calculate the following ratios (write the fraction and then round to the nearest tenth): Triangle 1 Triangle 2 Triangle 3 Leg opposite <A Leg adjacent <A Leg opposite <B Leg adjacent <B Leg opposite <C Leg adjacent <C Leg adjacent <A Hypotenuse Leg adjacent <B Hypotenuse Leg adjacent <C Hypotenuse Leg opposite <A Hypotenuse Leg opposite <B Hypotenuse Leg opposite <C Hypotenuse 4. Now on your calculator, locate the sin, cos, and tan keys. Use your calculator to find the following answers: tan 31 = cos 31 = sin 31 = 5. What do you notice? (Think hard, you’ll share this with the class)