University:
Felician University
Course:
MATH-160 | College Algebra
Academic year:

2022
Views:

380

Pages:

10
Author:

SpaceCadet101

/ Trigonometric Ratios Chief SOHCAHTOA says, "Use my name to remember the three basic trigonometric ratios." Opposite =----- Sine Hypotenuse Adjacent Cosine= -----Hypotenuse Opposite Tangent=----Adjacent Use the triangles below to match the trigonometric ratios. Your answers will help you to find the name of the first woman in American history to receive а patent. А 8 D 17 �� 1. 6. 11. 16. sin o• tan<С· sin< А C0S\ ;:;�� :а�; L-.:- / so тн нт ОР 42.5 tti 22.5 ft 55.4 in. /9.42 ·····••1 72" 700 mi • � � ЕВ EL .5 ft. 128.1 ft IN/ QU-- МЕ 92.51... IT 38.1 m 1 АВ ✓ , �) ....... IG 1 -0� 4.7 ст UP / '-МU/ 17.1 fЪ 9-2.0 i . J / 00, 16.1'mi 2Е8.57 ЕТ сн он 95.32 5.7 t11. 1••····· Dm1FFYNITl8N DБC8DБI! -- •ilio�--�------·-----------31° 32° 48° 45° 6° 29° 53° 6° 68° 27° 6° 6° 37° 5° 37" 5° 48° 37" 23° 8° 31° ..,.., •�№�---------------' ° ° ° ° ° ° ° ° ° ° ° ° ° 70 42 4 4 4 34 47" 42 4 72 31 32 48 37" 68 Find the measure of the a�gle that is marked (round to the nearest degree). Each time your answer appears in the code, write the vertex letter above -lt. 8 in. �34ft D 80 ft 1�n т � А ........_.______......, 25 km 6 mi t7 &! 18 ft W...---т-----,....., 9ft К 40 m () • f An ac cess ramp rises 3.2 ft over а distance of 30 ft. What is the angle of the ramp with the horizontal? Е 30 ft =:]3.2ft S -=-т--------,ц-, 1000 ft • -.1 2.7mi "51 N Тhе top of а 20-ft waterslide is 16 ft above the ground. ,t: 20ft What angle does Ф� the slide ma ke with � the vertical ladder? - J �_V? i ' I х Тracking а Rocket Launc . At what angle must а 3 km � camera at point Р Ье aimed t o phot?gr�h ...f:............ ................... , "" а roc kеt а t pom t .л.r f---5 km ---i - /. / А plane descends 1 ООО ft while flying 2. 7 mi. What is the angle of descent? (1 mi = 5280 ft) . ,,, What Do Уои Call а Row of Largв Animals . gвparating Two Yards?�':- Partner А should do the left side and Partner В the right side. Cross out the letter above each correct answer. The remaining letters will answer the title question. (Some answers are rounded.) Find the measure of the side or angle labeled х. ф ф х ,, - ф � . . ф n.�in. 9;� -- - ф х х 380mm ф 322mm "• r ф А telescope is mounted оп а tripod Solve. , 5 ft above the ground and 20 ft from а flagpole. The telescope must Ье rotated 48° from horizontal to see the top _ 48 ow tall 2::��:�? H _ �...... �-�J.�� ... ... 0 f; :� 20ft .,. ф А skier drops 800 vertical feet while skiing 1300 ft. What is the angle of the ski slope with the horizontal? 1 fD А submarine dives at an angle of 12° to the surface of the water. The submarine travels at а speed of 740 feet per minute. 12° About how deep is the submarine х � after 5 min? ф The roof°of а ski cabln has а steep pitch to help snow sHde off. What angle does the roof make with the horizontal? C\J ('() со Cf) lf) C\J 1'-- ,:t:: о tn tn о (\J (О о ,..-; L() C\J ['-.. (\J _,,,, ' : :, ф А submarine·dives at an angle of 14 ° to the surface of the water. The submarine travels at а speed of 720 feet per minute. About how deep is the submarine after 5 min? �х sub а steep pitch to help snow sHde off. What angle does the roof make with the horizontal? L Е D F ,:t:: . - 5f ф The roof of а ski cabin has - о , f €!) А telescope is mounted on а tripod 5 ft above the ground and 18 ft from а flagpole. The telescope must Ье rotated 49° from horizontal to see the top о of the flagpole. ow tall .... . .........5. is the flagpole? H �� 1&-fu ..... 1 • • .;_ ! ф А skier drops 700 veгt1ca1 feet while skiing 1200 ft. What is the angle of the ski s]ope with the horizontal? sub о j 7;� x_� -L......L..____ 1-J Solve.- 33� Find the measure of the side or angle labeled х. s () ,;;:!< 1'-- -, т т н � ,:t:: � со � lf) ,...... ('() C\J (j) (О 1'-- Е R � � ,:t:: ,:t:: ,..-; 1'-- СХ) со 00 ,-; со � (j) 1'-- lf) С'3 о N R А с о о С) СХ) о L() lЛ ['-.. <.О С') L.') (О s L() ,:t:: (\J (\J G Е d (О С') s () m <.О т о ,...... С') Class Name Date 1 '.� Practice Form G Trigonometry Write the ratios for sin Х, cos Х, and tan Х. S t1X-== 2. х 1. s� (ff;;> у � 12 z у 8 16 � 1\. 'К. ;; '/7- : �/2- z svз х �-:. 3. х 8� у 4 V5 5 z � �- � Find the value of х. Round to the nearest tenth. 4. х 7 ' ° 5.4 х . 29 б.� лх � 33 8. An escalator at а shopping center is 200 ft 9 in. long, and rises at an angle of 15 ° . What is the vertical rise of the escalator? Round to the nearest inch. 9. А 12-ft-long ladder is leaning against а wall and makes а 77° angle with the ground. How high does the ladder reach on the wall? Round to the nearest inch. , , , 10. А straight ramp rises at an angle of 25.5 and has а base 30 ft long. How high is the ramp? Round to the nearest foot. ° Find the value of х. Round to the nearest degree. 11. 24 � 9 13. Ц) 14. 121,., . ;..,,' )(. Df -:: 2/3 =- Cs/1- Practice Form G (continued) Trigonometry --- 15. The lengths ofthe diagonals of а rhombus are 4 in. and 7 in. Find tl1e measures ofthe angles ofthe rhombus to the nearest degree. 16. The lengths ofthe diagonals of а rhombus are 5 in. and 8 in. Find the measures ofthe angles ofthe rhombus to the nearest degree. ,; • / 't � ., , _,, Find the values of w and then х. Round lengths to the nearest tenth and angle measures to the nearest degree. 5 17. 18- .-, -="��· 6 5 � 5.5 � 19. Writing Explain why tan 45 ° = 1. - s l,v s l The sine, cosine, and tangent ratios each have а reciprocal ratio. The reciprocal ratios are cosecant (csc), secant ( sec), and cotangent (cot). Use L.DEF and the definitions below to write each ratio. l l l cotX - tanX secX - cosX cscX - sinX 20. csc D 21. secD 22. cot D 23. csc F 24. sec F 25. cot F О 8 Е identity is an equation that is true for all the allowed values ofthe variaЬle. Use what you know about trigonometric ratios to show that the equation . 'd . cot х = cosX sin Х 1s an 1 entity. 26. An 27. Reasoning Does sinA + sin В= sin (А+ В) when О< А+ В< 90? Explain уо r reasoning. 28. А right triangle has а hypotenuse oflength 10 and one leg oflength 7. Find the length ofthe other leg and the measures ofthe acute angles in the triangle. Round your answers to the nearesLtenth ;,-, � - 29. А right triangle has а 7 [.,t =t'L -: , - . � ang Fthafmeasures 28. The leg opposite fue 28 angle ,,,, и • ° measures 13. Find the length ofthe other leg and the hypotenuse. Round your answers to the nearest tenth. "2- L I0 2- � /()0 t:::.. -:r. 1] Practice Form G Angles of Elevation and Depression Describe each angle as it relates to the situation in the diagram. 1. Ll 2. L2 3. LЗ 4. L4 5. L5 6. L6 7. L7 8. L8 •�,,,�( I - - - -5- -------� - - -6 , '' 7 ______ _____ _ '' в', Find the value of х. Round to the nearest tenth of а unit. 10. 9. ..................... х 125 ft 30 ° 40 ° 300 ft х 12. 11. 60 ft � 25° �х 13. А pei-son is standing 40 ft fi-om а flagpole and can see the top of the pole at а 35° angle of elevation. The pei-son's еуе level is 4 ft fi-om the gi-ound. What is the height of the flagpole to the neai-est foot? 14. An eagle pei-ched 40 ft up in а tree looks down at а 35 ° angle and spots а vole. How far is the vole from the eagle to the nearest tenth of а foot? )[ l) Practice Form G (continued) Angles of Elevation and Depression 15. You stand.40 ft from а tree. The angle of elevation from your eyes (5 ft above the ground) to the top ot'the tree is 47° . How tall is the tree? Round your answer to the nearest t·oot. Find the value of х. Round to the nearest tenth of а unit. 16. 17. Sr-nlt= X. 18. ,,,;;:,,,2,2- х 4 := 19. 12,000 ft 1� х 20. An airplane is flying at an altitude of 10,000 ft. The airport at which it is scheduled to land is 50 mi away. Find the average angle at which the-airplane must descend for landing. Rou11d уош answer to the nearest degree. - , 7 21. А lake measures 600 ft across. А lodge stands оп one shor� From your point оп the opposite shore, the angle of elevation to the top of the lodge is 4°. How high above the lake does the lodge stand? Round your answer to the nearest foot. 22. А library needs to build an access ramp for wheelchairs. The main entrance to the library is 8 ft above sidewalk level. If the architect designs the slope of the ramp in such а way that the angle of elevation is 5° , how long must the access ramp Ье? Round your answer_ to the nearest foot. /, - Algebra The angle of elevation е from А to В and the angle of depression d fro В to А are given. Find the measure of each angle. 23. е: (Зх + 6) 0 d: (х + 20) 0 , 25. е: (Зх - 4)0 d: 2(х + 7) 0 , . 24. е: (6х + 3)0 d: 3(-х-+ 6)0 , 26. e':fSx - 8) 0 d: З(х + 4).,. , , I ) 8 (,)С+3 - 3)(...+ 1i sx.�11=;> с х_ 5