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Identify the following trigonometric ratios. 77AA D Deeffiinnee tthhee tthhrreeee ttrriiggoonnoom meettrriicc rraattiiooss ((ssiinnee,, ccoossiinnee,, ttaannggeenntt)) iinn tteerrm mss ooff aa rriigghhtt ttrriiaannggllee. 1. ____________= Opposite Adjacent 2. cos = Opposite ________ 3. tan____=_________ Hypotenuse Find the value of the trigonometric ratio for the following 2 problems and round to the nearest tenth. 77BB FFiinndd tthhee vvaalluuee ooff tthhee ttrriiggoonnoom meettrriicc rraattiiooss ffoorr aa ggiivveenn aannggllee ooff aa ttrriiaannggllee.. 4. sin C 5. tan A Define the values of sin, cos, and tan for the following special right triangles 77C C FFiinndd tthhee vvaalluueess ooff tthhee ttrriiggoonnoom meettrriicc rraattiiooss ffoorr aa 3300ooo,, 4455ooo,, 6600ooo,, aanndd 9900oooaannggllee. 6. sin H=_____ cos K=_____ tan H=_____ 7. sin F = _____ cos F = _____ tan F = _____ sin G = ____ cosG = ____ tan G = ____ Solve the following real world problems using trigonometric functions (determine what you have and what you need). 77D D SSoollvvee rreeaall w woorrlldd pprroobblleem mss iinnvvoollvviinngg iinnddiirreecctt m meeaassuurreem meenntt uussiinngg tthhee ttrriiggoonnoom meettrriicc rraattiiooss.. 8. A research vessel surveying the ocean floor for an ancient sunken Greek ship. The ship’s radar sounded an object resting on the bottom of the ocean 900 feet diagonally from the ship’s hull. The angle of depression from the ocean’s surface to the object is 45°. Determine how many feet the ship must move forward to be located directly over the mystery object AND what is the depth of the object from the ocean’s surface. Using your trigonometry chart find the values of the sides or angles (value of variable “x”) of the following problems, round to the nearest tenth. 77EE EExxppllaaiinn tthhee nnoottiioonn ooff aann iinnvveerrssee ttrriiggoonnoom meettrriicc rraattiioo,, aanndd hhoow w iitt iiss uusseedd ttoo ssoollvvee ttrriiggoonnoom meettrriicc eeqquuaattiioonnss 77FF FFiinndd tthhee m miissssiinngg ssiiddeess aanndd aanngglleess ooff aa ttrriiaannggllee uussiinngg tthhee ttrriiggoonnoom meettrriicc rraattiiooss aanndd tthheeiirr iinnvveerrsseess.. 9. 10. 12. 13. 11. 14. Use the Pythagorean theorem to find the length of the missing side. 77II D Deevveelloopp aanndd pprroovvee tthhee PPyytthhaaggoorreeaann iiddeennttiittyy.. 15. 16. 17. Use the tangent and the Pythagorean theorem to find missing lengths of the following equations (use tan to solve for x first, then use Pythagorean theorem to solve for hypotenuse). 77JJ U Ussee tthhee ttaannggeenntt iiddeennttiittyy aanndd tthhee PPyytthhaaggoorreeaann iiddeennttiittyy ttoo ssoollvvee ttrriiggoonnoom meettrriicc eeqquuaattiioonnss.. 18. 19. 20.