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Math 2 Lesson 5-1: Right Triangle Trigonometry Name ___________________________ Date __________________________ Learning Goals: I can use the Pythagorean Theorem to solve for an unknown side length of a right triangle. I can use the characteristics of similar figures to justify the trigonometric ratios. I can define the following trigonometric ratios for acute angles in a right triangle: sine, cosine, and tangent. I can calculate sine, cosine and tangent ratios for acute angles in a right triangle when given two side lengths. I can understand that if cos A = sin B, then A and B are complementary angles. I can explain this using a picture of a right triangle. I can use the angle measures to estimate side lengths. I can use side lengths to estimate angle measures. I. Prerequisite Skills for Trigonometry: II. What is Trigonometry? Trigonometry is Vocabulary and symbols: Opposite leg Adjacent leg Hypotenuse Acute angles α Right angle Pythagorean Theorem Ratio Complementary angles β θ OVER Page 2 III. Ratios of Sides in Right Triangles 8.2 cm 4.5 cm 4.2 cm 3.1 cm 1.7 cm 7.6 cm 10.9 cm 6.6 cm 10.1 cm 7.1 cm 2.7 cm 4.1 cm Verify that the four triangles above are similar and write the similarity statements. Round to the nearest 1000th. Length of the leg opposite the 22° angle Length of the leg adjacent to the 22° angle Length of the hypotenuse ΔABC ΔDEF ΔHIJ ΔLMN Calculate the mean of each column. Length of opposite leg Length of opposite leg Length of adjacent leg ÷ ÷ ÷ Length of adjacent leg Length of hypotenuse Length of hypotenuse Page 3 1. On the calculator, press c and choose #5 Settings and #2 Document Settings. Next scroll down to Angle and choose Degree. Finally select Make Default. 2. Use your calculator to fill in the problems below: Round to 3 decimal places. sin(22o ) ________ cos(22o ) ________ tan(22o ) ________ Look back at your computations in the table. Where do you see these same values? 3. Based on your measurements and computations from this worksheet complete the following definitions: In any right triangle, where is NOT the right angle: sine side angle cosine side angle tangent side side angle angle 4. Mnemonic device to remember these ratios: 5. If you know a ratio of two side lengths, how can you find the acute angle measure? In the figure below A is a right angle. Round to 3 decimal places. Find the length of c using C. 5.8 cm 29◦ Find the length of c using B. What is the relationship between cos( B ) and sin(C ) ? Practice 1. Find the below ratios: 2. Solve for x 3. Solve for mA 1a. sin X 1b. tan X 1c. cos Z HOMEWORK: 7. mH ______ 8. mL ______ 7. cos1 0.48 __________ 8. sin 1 0.42 __________ 9. tan 1 0.5 __________ C. Solve for the variables. Round to the nearest 100th. OVER 4. 5. 6. 7.