9.5 Start Thinking. 9.5 Warm Up. 9.5 Cumulative Review Warm Up
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1 9.5 Strt Thinking In Lesson 9.4, we discussed the tngent rtio which involves the two legs of right tringle. In this lesson, we will discuss the sine nd cosine rtios, which re trigonometric rtios for cute ngles tht involve the lengths of leg nd the hpotenuse of right tringle. Consider wht ou know out the length of the hpotenuse of n right tringle. If we define the rtios s shown elow, wht conclusions cn ou mke out the vlues of the sine nd cosine of n cute ngle in right tringle? Sine of n cute ngle = length of side opposite ngle length of hpotenuse Cosine of n cute ngle = length of side djcent to ngle length of hpotenuse 9.5 Wrm Up Find the vlue of. Round our nswer to the nerest tenth Cumultive Review Wrm Up Find the coordintes of the circumcenter of the tringle with the given vertices. 1. A( 4, 2 ), B( 8, 5 ), C ( 8, 2) M( 3, 0, ) N( 2, 6, ) P( 1, 4) 3. F( 3, 2, ) D( 0, 0, ) R( 8, 4) 4. X( 10, 3 ), Y( 2, 7 ), Z( 2, 5) 310 Geometr Copright Big Ides Lerning, LLC
2 Nme Dte 9.5 Prctice A In Eercises 1 nd 2, find sin J, sin K, cos J, nd cos K. Write ech nswer s frction nd s deciml rounded to four plces. 1. J L 30 K L 12 K J In Eercises 3 6, write the epression in terms of sine or cosine. 3. sin cos cos sin 37 In Eercises 7 9, find the vlue of ech vrile using sine nd cosine. Round our nswers to the nerest tenth r s 10. Which sttement cnnot e true? Eplin. B A. sin A = 0.5 B. sin A = C. sin A = D. sin A = 3 4 A C Not drwn to scle 11. The ngle of depression is 11 from the ottom of ot to deep se diver t depth of 120 feet. Find the distnce the diver must swim up to the ot to the nerest foot. ft 120 ft Copright Big Ides Lerning, LLC Geometr 311
3 Nme Dte 9.5 Prctice B In Eercises 1 nd 2, find sin R, sin S, cos R, nd cos S. Write ech nswer s frction nd s deciml rounded to four plces. 1. R R 12 S T 48 S T In Eercises 3 5, write the epression in terms of sine nd/or cosine. 3. sin 7 4. cos tn 60 In Eercises 6 8, find the vlue of ech vrile using sine nd cosine. Round our nswers to the nerest tenth. 6. p q Find the perimeter of the figure shown. Round our nswer to the nerest centimeter cm 10. You use n etension ldder to repir chimne tht is 33 feet tll. The length of the etension ldder rnges in one-foot increments from its minimum length to its mimum length. For sfet resons, ou should lws use n ngle of out 75.5 etween the ground nd our ldder.. Your smllest etension ldder hs mimum length of 17 feet. How high does this ldder sfel rech on the chimne? Round our nswer to the nerest tenth of foot. 33 ft. You plce the ldder 3 feet from the se of the chimne. How mn feet long should the ldder e? Round our nswer to the nerest foot. c. To rech the top of the chimne, ou need ldder tht reches 30 feet high. How mn feet long should the ldder e? Round our nswer to the nerest foot Geometr Copright Big Ides Lerning, LLC
4 Nme Dte 9.5 Enrichment nd Etension The Sine nd Cosine Rtios In Eercises 1 nd 2, find the missing vrile(s). Round our nswers to the nerest thousndths. 1. C A B 17 cm z w 3. In right RTX, sin R = 5. If the hpotenuse of the tringle is 117 units, wht is the tringle s perimeter? 4. Find the perimeter of the isosceles trpezoid. Round our nswer to the nerest tenth. 25 in. 10 in In right ABC, m B = 90 nd m A = 30. Wht is the rtio of the longest leg to the hpotenuse? In Eercises 6 nd 7, use the digrm t the right Write n epression for ( sin ) ( cos ) + in terms of,, nd z. Then use the Pthgoren Theorem (Theorem 9.1) to simplif the epression. z 7. Suppose sin = 0.6. Wht is the vlue of cos? Copright Big Ides Lerning, LLC Geometr 3
5 Nme Dte 9.5 Puzzle Time Wht Is A Computer Virus? Write the letter of ech nswer in the o contining the eercise numer. Complete the sentence. 1. The nd cosine rtios re trigonometric rtios for cute ngles tht involve the lengths of leg nd the hpotenuse of right tringle. The sine of n ngle is equl to the of its complement. 3. The cosine of n ngle is equl to the sine of its. 4. The ngle tht downwrd line of sight mkes with horizontl line is clled the ngle of. Write the sine in terms of cosine. 5. sin sin sin 25 Write the cosine in terms of sine. 8. cos cos cos 71 Answers L. sin 54 M A. tngent M. cos 48 N. cosine T. sine E. sin 19 A. sin 75 L. cos 12 I A S S. cos 65 S. cos 42 O. elevtion N. supplement L N. depression U. cos 35 R Find the indicted vlue using the digrm. Round to four deciml plces. 11. = 17, = 15, c = 8; Find the sine X c Y V. sin I. complement E of ngle X. Z D G = 26, = 10, c = 24; Find the cosine of ngle Z.. = 25, = 24, c = 7; Find the cosine of ngle X. 14. = 15, = 9, c = 12; Find the sine of ngle Z. 15. = 22, m Z = 41 ; Find. 16. = 22, m Z = 41 ; Find c Geometr Copright Big Ides Lerning, LLC
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