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February 06, 2017 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) 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 06, 2017 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 Example 1: Label the triangle while focusing on angleB. February 06, 2017 1. Go to my website (www.tinyurl.com/WrightGeometry) 2. Scroll down to Unit 8, Lesson 1 and select the Tangent Ratio Link. 3. Select the 3rd check box 4. Answer the following questions. Q1: What side lengths are being highlighted in relation to the angle? Q2: Select an angle with the blue slider and then change the size of the triangle using the dots. What do you notice about the ratio being calculated? Q3: Select a different angle with the blue slider and then change the size of the triangle using the dots. What do you notice about the ratio being calculated? Q4: If the measure of the angle is changed, what happens to the value of the ratio? February 06, 2017 Example 2: What does Example 2 allow us to say about any right triangle with an angle congruent to angle A? February 06, 2017 Tangent Ratio - relates the opposite leg of an angle to its adjacent leg this can be shortened to.... 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 angle that you last used in GeoGebra 3. Hit enter. 4. Compare the value to what you see on GeoGebra. * The number in the calculator is telling you the ratio of the opposite leg to the adjacent leg February 06, 2017 Example 3: Write the tanR and tan T as ratios. Example 4: February 06, 2017 Example 5: Example 6: In the calculator type tan(90). What happens? Can we take the tangent of a 90 degree angle? February 06, 2017