In Exercises 1 and 2, use the diagram at the right. 1. Use the diagram to explain what is meant by the sine, the cosine, and the tangent of A.

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1 Page 5 of 9 GUIE PRTIE Vocabular heck oncept heck Skill heck In Eercises 1 an 2, use the iagram at the right. 1. Use the iagram to eplain what is meant b the sine, the cosine, an the tangent of. 2. ERROR NLYSIS stuent sas that sin > sin because the sie lengths of EF are greater than the sie lengths of. Eplain wh the stuent is incorrect. In Eercises, use the iagram shown at the right to fin the trigonometric ratio. 7 7 F E. sin 4. cos 5 5. tan. sin 7. cos. tan 4 9. ESLTORS One earl escalator built in 19 rose at an angle of 25. s shown in the iagram at the right, the vertical lift was 7 feet. Estimate the istance a person travele on this escalator. 7 ft PRTIE N PPLITIONS STUENT HELP Etra Practice to help ou master skills is on p. 20. FINING TRIGONOMETRI RTIOS Fin the sine, the cosine, an the tangent of the acute angles of the triangle. Epress each value as a ecimal roune to four places. 10. R X T 45 S Z Y STUENT HELP HOMEWORK HELP Eample 1: Es , 2 Eample 2: Es , 2 Eample : Es. 4 Eample 4: Es. 4 Eample 5: Es Eample : Es Eample 7: Es E 14. G 1 J F LULTOR Use a calculator to approimate the given value to four ecimal places. 1. sin cos 1 1. tan sin cos tan sin 7 2. cos 24. tan cos 2. sin tan H J L 4 5 K 52 hapter 9 Right Triangles an Trigonometr

2 Page of 9 USING TRIGONOMETRI RTIOS Fin the value of each variable. Roun ecimals to the nearest tenth t 4 2 s s r u w 70 v t 22 FINING RE Fin the area of the triangle. Roun ecimals to the nearest tenth m 45 4 cm 0 12 m 0 11 m FOUS ON PPLITIONS 7. WTER SLIE The angle of elevation from the base to the top of a waterslie is about 1. The slie etens horizontall about 5.2 meters. Estimate the height h of the slie. h 5.2 m 1 WTER SLIE Even though riers on a water slie ma travel at onl 20 miles per hour, the curves on the slie can make riers feel as though the are traveling much faster. REL LIFE. SURVEYING To fin the istance from a house on shore to a house on an islan, a surveor measures from the house on shore to point, as shown in the iagram. n instrument calle a transit is use to fin the measure of. Estimate the istance. 9. SKI SLOPE Suppose ou stan at the top of a ski slope an look own at the bottom. The angle that our line of sight makes with a line rawn horizontall is calle the angle of epression, as shown below. The vertical rop is the ifference in the elevations of the top an the bottom of the slope. Fin the vertical rop of the slope in the iagram. Then estimate the istance a person skiing woul travel on this slope. 40 m 42 angle of epression 20 elevation 5500 ft elevation 501 ft vertical rop 9.5 Trigonometric Ratios 5

3 Page 7 of 9 FOUS ON PPLITIONS 40. SIENE ONNETION Scientists can measure the epths of craters on the moon b looking at photos of shaows. The length of the shaow cast b the ege of a crater is about 500 meters. The sun s angle of elevation is 55. Estimate the epth of the crater. sun s ra m LUNR RTERS ecause the moon has no atmosphere to protect it from being hit b meteorites, its surface is pitte with craters. There is no win, so a crater can remain unisturbe for millions of ears unless another meteorite crashes into it. REL LIFE 41. LUGGGE ESIGN Some luggage pieces have wheels an a hanle so that the luggage can be pulle along the groun. Suppose a person s han is about 0 inches from the floor. bout how long shoul the hanle be on the suitcase shown so that it can roll at a comfortable angle of 45 with the floor? 42. UYING N WNING Your famil room has a sliing-glass oor with a southern eposure. You want to bu an awning for the oor that will be just long enough to keep the sun out when it is at its highest point in the sk. The angle of elevation of the sun at this point is 70, an the height of the oor is feet. bout how far shoul the overhang eten? 2 in. 45 ft 70 0 in. sun s ra RITIL THINKING In Eercises 4 an 44, use the iagram. 4. Write epressions for the sine, the cosine, an the tangent of each acute angle in the triangle. 44. Writing Use our results from Eercise 4 to eplain how the tangent of one acute angle of a right triangle is relate to the tangent of the other acute angle. How are the sine an the cosine of one acute angle of a right triangle relate to the sine an the cosine of the other acute angle? c b a 45. TEHNOLOGY Use geometr software to construct a right triangle. Use our triangle to eplore an answer the questions below. Eplain our proceure. For what angle measure is the tangent of an acute angle equal to 1? For what angle measures is the tangent of an acute angle greater than 1? For what angle measures is the tangent of an acute angle less than 1? 4. ERROR NLYSIS To fin the length of Æ in the iagram at the right, a stuent writes 1 tan 55 =. What mistake is the stuent making? Show how the stuent can fin. (Hint: egin b rawing an altitue from to Æ.) hapter 9 Right Triangles an Trigonometr

4 Page of PROOF Use the iagram of. omplete the proof of the trigonometric ientit below. (sin ) 2 + (cos ) 2 = 1 GIVEN sin = a c, cos = b c c b a PROVE (sin ) 2 + (cos ) 2 = 1 Statements 1. sin = a c, cos = b c 2. a 2 + b 2 = c 2 2. a 2 b + c 2 = 1 c 2 4. a c 2 + b c 2 = 1 5. (sin ) 2 + (cos ) 2 = 1 Reasons 1.? 2.?.? 4. propert of eponents 5.? Test Preparation EMONSTRTING FORMUL Show that (sin ) 2 + (cos ) 2 = 1 for the given angle measure. 4. m = m = m = m = PROOF Use the iagram in Eercise 47. Write a two-column proof of the sin following trigonometric ientit: tan = c os. 5. MULTIPLE HOIE Use the iagram at the right. Fin. cos 25 sin 25 tan 25 sin 25 E cos MULTIPLE HOIE Use the iagram at the right. Which epression is not equivalent to? sin 70 cos 20 tan 20 tan 20 E tan E hallenge EXTR HLLENGE PRE You are at a parae looking up at a large balloon floating irectl above the street. You are 0 feet from a point on the street irectl beneath the balloon. To see the top of the balloon, ou look up at an angle of 5. To see the bottom of the balloon, ou look up at an angle of 29. Estimate the height h of the balloon to the nearest foot ft h 9.5 Trigonometric Ratios 55

5 Page 9 of 9 MIXE REVIEW 5. SKETHING ILTION PQR is mappe onto P Q R b a ilation. In PQR, PQ =, QR = 5, an PR = 4. In P Q R, P Q =. Sketch the ilation, ientif it as a reuction or an enlargement, an fin the scale factor. Then fin the length of Q R an P R. (Review.7) 57. FINING LENGTHS Write similarit statements for the three similar triangles in the iagram. Then fin QP an NP. Roun ecimals to the nearest tenth. (Review 9.1) PYTHGOREN THEOREM Fin the unknown sie length. Simplif answers that are raicals. Tell whether the sie lengths form a Pthagorean triple. (Review 9.2 for 9.) M 15 7 N q P QUIZ 2 Self-Test for Lessons 9.4 an 9.5 Sketch the figure that is escribe. Then fin the requeste information. Roun ecimals to the nearest tenth. (Lesson 9.4) 1. The sie length of an equilateral triangle is 4 meters. Fin the length of an altitue of the triangle. 2. The perimeter of a square is 1 inches. Fin the length of a iagonal.. The sie length of an equilateral triangle is inches. Fin the area of the triangle. Fin the value of each variable. Roun ecimals to the nearest tenth. (Lesson 9.5) HOT-IR LLOON The groun crew for a hot-air balloon can see the balloon in the sk at an angle of elevation of 11. The pilot raios to the crew that the hot-air balloon is 950 feet above the groun. Estimate the horizontal istance of the hot-air balloon from the groun crew. (Lesson 9.5) Not rawn to scale groun crew ft 5 hapter 9 Right Triangles an Trigonometr