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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
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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
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Consider the following 30-60-90 triangles A B C D F E H J K c = 2 b = a = 1 f = 4 d = 2 e =j = h = 3 k = 6 Compare the length of the leg opposite the 30 angle with the length of the hypotenuse in each triangle.
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By using similar triangles, we can see that in every 30-60-90 triangle
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Engineers and Scientist have found it convenient to formalize these relationships by naming the ratios of sides. You should memorize these three basic ratios.
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Example 1 Find: a. b. AC B 5 12 c
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Example 2 Find the three trigonometric ratios for angles A and B AC B 3 4 5
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Example 3 Triangle ABC is an isosceles triangle, find sin C A C B 13 10 13
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Example 4 Use the fact that tan 40 is approximately 0.8391 to find the height of the tree to the nearest foot. 50 ft h 40
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Summary Summarize in your own words how to find the sin, cos, and tangent of a 30-60-90 triangle. Homework: Worksheet 9.9
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