1. Obj. 40 Trigonometry The student is able to (I can): For any right triangle Define the sine, cosine, and tangent ratios and their inverses Find the measure of a side given a side and an angle Find the measure of an angle given two sides Use trig ratios to solve problems

2. By the Angle-Angle Similarity Theorem, a right triangle with a given acute angle is similar to every other right triangle with the same acute angle measure. This means that the ratios between the sides of those triangles are always the same. Because these ratios are so useful, they were given names: sine cosine and sine, cosine, tangent. tangent These ratios are used in the study of trigonometry. 3. oppositehypotenuseadjacentAsineleg opposite A sine of A = sinA = hypotenusecosinecosine of A = cosA =tangentleg opposite A tangent of A = tanA = leg adjacent to Aleg adjacent to A hypotenuse 4. We can use the trig ratios to find either missing sides or missing angles of right triangles. To do this, we will set up equations and solve for the missing part. In order to figure out the sine, cosine, and tangent ratios, we can use either a calculator or a trig table. 5. To use the calculator to find tan 51: From a New Document, press the key: Use the right arrow key ( ) to select tan () and press : 6. Type 5I and hit :To use the calculator on your phone: Turn your phone landscape to access the scientific calculator. Type the angle in first, then select sin. 7. To use the trig table to find cos 52: Locate 52 on the table. Scan over to the Cos column and find the value. cos 52 = .6157 8. You will be expected to memorize these ratios. There are many hints out there to help you keep them straight. The most common is SOH-CAH-TOA , where SOH-CAHOp p Sin = HypAdj Cos = HypOp p Tan = AdjA mnemonic I like is Some Old Hippie Caught Another Hippie Trippin On Acid. Or Silly Old Hitler Couldnt Advance His Troops Over Africa. 9. ExamplesI.Use the triangle to find the following ratios. A 8 C1.sin A = _____2. cos A = _____ 3. tan A = _____17 B 15 10. ExamplesI.Use the triangle to find the following ratios. A 81.15 17 sin A = _____8 17 2. cos A = _____ 15 8 3. tan A = _____C17 B 15 11. ExamplesI.Use the triangle to find the following ratios. A 8 C4. sin B = _____ 5. cos B = _____ 6. tan B = _____17 B 15 12. ExamplesI.Use the triangle to find the following ratios. A 88 17 4. sin B = _____ 15 17 5. cos B = _____ 8 15 6. tan B = _____C17 B 15 13. ExamplesII.Find the lengths of the sides to the nearest tenth. x (opp)1.15 (adj)58x sin58 = 15 x = 15sin58 12.7 2.x 26 x = 26cos 46cos 46 =26 (hyp) 46 x (adj) 18.1