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February 11, 2016 Unit 9 Lesson 1 Tangent Ratio, part 1 New facts often trigger new ideas. - Alex F. Osborn (fun fact: he popularized group brainstorming as a creativity problem-solving technique) February 11, 2016 Trigonometry - "Study of triangles" To work with trigonometry we need a right triangle. We focus on one of the acute angles in the triangle. February 11, 2016 Terminology Hypotenuse - side opposite the right angle Opposite Leg - the leg that does not form the angle Adjacent Leg - the leg that does form the angle February 11, 2016 Example 1: Label the triangle while focusing on angleB. 0 February 11, 2016 90 90 100 80 110 120 70 130 60 140 50 0° 40 150 30 160 20 10 0 170 180 February 11, 2016 February 11, 2016 February 11, 2016 Example 2: February 11, 2016 What does Example 2 allow us to say about any right triangle with an angle congruent to angleA? February 11, 2016 Tangent Ratio - relates the opposite leg of an angle to its adjacent leg this can be shortened to.... February 11, 2016 Using a calculator: Always check the mode and place calculator in "degrees" In the calculator: 1. Hit the tan button 2. Type your measure of angleA from the worksheet and close the parenthesis 3. Hit enter. 4. Compare the value you found in Step 4 on the WS * The number in the calculator is telling you the ratio of the opposite leg to the adjacent leg February 11, 2016 Example 3: Write the tanR and tan T as ratios. February 11, 2016 Example 4: In the calculator type tan(90). What happens? Can we take the tangent of a 90 degree angle? February 11, 2016