# Lesson 12.1 Right Triangle Trigonometry

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1 Lesson 12.1 Right Tringle Trigonometr 1. For ech of the following right tringles, find the vlues of sin, cos, tn, sin, cos, nd tn. (Write our nswers s frctions in lowest terms.) Drw right tringle for ech problem. Lbel the sides nd ngles with the given mesures, then solve to find the unknown vlue. Round our nswers to the nerest tenth. cos 27 r 8.5 tn S c. cos 52 z 3 z 3. For ech tringle, write n eqution to clculte the lbeled mesure. Then, solve the eqution. b c Discovering dvnced lgebr More Prctice Your Skills HPTER Ke urriculum Press

2 Lesson 12.2 The Lw of Sines 1. Solve ech eqution for Give n ect nswer nd n pproimte nswer. Round to the nerest tenth. sin 75 sin 20 9 b sin 95 sin 5 b.2 c. sin 32. sin b 2. Find the unknown ngle mesures nd side lengths. Round to the nerest tenth. 5. cm b mm c Determine the number of tringles with the given prts. (Do not find the missing side lengths nd ngle mesures.) 50, b 22. cm, c 27.2 cm 8, 25 cm, c 32 cm. ship is siling due est. t certin point, the cptin observes lighthouse t n ngle of 32 clockwise from north. fter the ship sils 28.0 km frther, the sme lighthouse is t n ngle of 310 clockwise from north. Drw digrm t right to illustrte this sitution. Let be the point where the first lighthouse observtion is mde, be the point where the second observtion is mde, nd be the loction of the lighthouse. Include ll given informtion in our digrm. Use the Lw of Sines to find the distnce between the lighthouse nd the ship t the time of the first observtion. c. Use the Lw of Sines to find the distnce between the lighthouse nd the ship t the time of the second observtion. 7 HPTER 12 Discovering dvnced lgebr More Prctice Your Skills

3 Lesson 12.3 The Lw of osines 1. Solve for b nd. ssume b is positive. b (1)(29) cos (.0)(5.1) cos 2. Use the given vlues to write n eqution for the unknown mesure. Then solve the eqution. Give n ect nswer nd n pproimte nswer. Round to the nerest tenth. b 9 5 c. 3.5 c 12 b 3 b c 82.5 c c b 3. Stte whether ou would use the Lw of Sines or the Lw of osines to solve ech problem. Given the mesures of two ngles of tringle nd the length of one of the sides tht is not between them, find the length of one of the other two sides. Given the lengths of ll three sides of tringle, find the mesure of the smllest ngle.. Find unknown ngle mesures nd side lengths. Round to the nerest tenth cm c 12.8 cm.9 cm 7.5 cm 3.8 cm 5. Use the Lw of osines to find the mesure of the lrgest ngle of tringulr grden whose sides mesure 12.5 ft, 19.8 ft, nd 15.7 ft. Discovering dvnced lgebr More Prctice Your Skills HPTER 12 75

4 Lesson 12. Etending Trigonometr 1. Sketch ech ngle in the coordinte plne. Then, find the mesure of the reference ngle for ech ngle c Find the trigonometric vlue requested for ech ngle. cos tn 3. Without using clcultor, determine whether ech vlue is positive or negtive. tn 100 sin 195 c. cos 70 d. sin 100 e. tn 20 f. cos 20 7 HPTER 12 Discovering dvnced lgebr More Prctice Your Skills

5 Lesson 12.5 Introduction to Vectors 1. Let 2, 3, b 3, 2, c 0, 1, nd d 1, 5. Evlute ech of the following epressions. b c b c. d d. 2c 2. Write ech vector in rectngulr form c Write ech vector in polr form. Round ech ngle mesure to the nerest degree. 2, 0 3, c. 2, 1. bot leves dock nd trvels 20 miles on bering of 58. It then turns nd trvels miles on bering of 352 to rech second dock. Drw sketch of the sitution. Find the ship s distnce nd bering from the initil dock. Round our nswers to the nerest tenth. Discovering dvnced lgebr More Prctice Your Skills HPTER 12 77

6 Lesson 12. Prmetric Equtions 1. rete tble for ech pir of prmetric equtions with the given vlues of t. t 5 t 3 t 2 1 t 3 t { 2, 1, 0, 1, 2} t {, 2, 0, 2, } 2. Write single eqution (using onl nd ) tht is equivlent to ech pir of prmetric equtions. (Ech eqution should epress in terms of.) t t 2 c. t 2 2 3t 2 2t 1 3t 2 3t 5 3. Use the grphs of f (t) nd g (t) to crete grph of s function of. t t. Hden rolls bll off the edge of the roof of 75 ft tll building t n initil velocit of.5 ft/s. Write prmetric equtions to simulte this motion. Wht eqution cn ou solve to determine when the bll hits the ground? c. When nd where does the bll hit the ground? (Round to the nerest hundredth.) 78 HPTER 12 Discovering dvnced lgebr More Prctice Your Skills

### MATHEMATICAL PRACTICES In the Solve It, you used what you know about triangles to find missing lengths. Key Concept Law of Sines

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