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Lesson 9.9 Introduction To Trigonometry Objective: After studying this section, you will be able to understand three basic trigonometric relationships This section presents the three basic trigonometric ratios sine, cosine, and tangent. The concept of similar triangles and the Pythagorean Theorem can be used to develop trigonometry of right triangles Consider the following 30-60-90 triangles J E B c=2 A b= 3 k=6 f=4 a=1 C D e= 2 3 h=3 d=2 F H j =3 3 K Compare the length of the leg opposite the 30 angle with the length of the hypotenuse in each triangle. a 1 ABC , 0.5 c 2 h 3 d 2 HJK , 0.5 DEF, 0.5 k 6 f 4 By using similar triangles, we can see that in every 30-60-90 triangle leg opposite30 1 hypotenuse 2 leg adjacent 30 3 hypotenuse 2 leg opposite30 1 3 leg adjacent 30 3 3 Engineers and Scientist have found it convenient to formalize these relationships by naming the ratios of sides. You should memorize these three basic ratios. leg opposite30 1 sine sin hypotenuse 2 leg adjacent 30 3 cosine cos hypotenuse 2 leg opposite30 1 3 tangent tan leg adjacent 30 3 3 Example 1 Find: a. b. cos A tan B B c 5 C 12 A Example 2 Find the three trigonometric ratios for angles A and B B 5 3 C 4 A Example 3 Triangle ABC is an isosceles triangle, find sin C A 13 B 13 10 C Example 4 Use the fact that tan 40 is approximately 0.8391 to find the height of the tree to the nearest foot. h 50 ft 40 Summary Summarize in your own words how to find the sin, cos, and tangent of a 30-60-90 triangle. Homework: Worksheet 9.9