Special Right Triangles


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1 Pge of 5 L E S S O N 9.6 Specil Right Tringles B E F O R E Now W H Y? Review Vocbulr hpotenuse, p. 465 leg, p. 465 You found side lengths of right tringles. You ll use specil right tringles to solve problems. So ou cn find the distnce softbll is thrown, s in E. 5. A digonl of squre divides it into two 90 tringles. In such tringle, the lengths of the legs re equl. Let represent the length of ech leg, nd let c represent the length of the hpotenuse. B the Pthgoren theorem, c , so c c 90 Tringle Words In 90 tringle, the length of the hpotenuse is the product of the length of leg nd 2. 2 Algebr hpotenuse legp 2 2 Emple Using 90 Tringle Gmnstics The mt used for floor eercises t gmnstics competition is squre with side length of 2 meters. A gmnst strts t one corner of the mt nd does tumbling routine long the digonl to the opposite corner. To the nerest meter, how long is the gmnst s pth? 2 m 2 m Solution The digonl divides the mt into two 90 tringles. The digonl is the hpotenuse of ech of the tringles. hpotenuse leg p 2 2 p 2 7 Rule for 90 tringle Substitute. Use clcultor. Answer The gmnst s pth is bout 7 meters long. Lesson 9.6 Specil Right Tringles 483
2 Pge 2 of 5 Note Worth You cn orgnize informtion bout right tringles in our notebook using concept mp like the one on p Tringle You cn divide n equilterl tringle in hlf s shown to mke two 90 tringles. In the digrm, the equilterl tringle hs side lengths of 2. Ech right tringle hs hpotenuse of length 2 nd shorter leg of length. Let b be the length of the longer leg. B the Pthgoren theorem, (2) 2 2 b 2. Then b , so b b Tringle Stud Strteg In 90 tringle, the shorter leg is opposite the ngle, nd the longer leg is opposite the ngle. Words In 90 tringle, the length of the hpotenuse is twice the length of the shorter leg. The length of the longer leg is the product of the length of the shorter leg nd 3. Algebr hpotenuse 2pshorter leg 2 longer leg shorter legp Emple 2 Using 90 Tringle Find the length of the hpotenuse nd the length of the longer leg of the tringle. The tringle is 90 tringle. The length of the shorter leg is 8 units.. hpotenuse 2pshorter leg 2p8 6 Answer The length of the hpotenuse is 6 units. b. longer leg shorter legp Answer The length of the longer leg is 8 3 units. 8 Checkpoint Find the unknown lengths. Write our nswer in simplest form Chpter 9 Rel Numbers nd Right Tringles
3 Pge 3 of 5 Emple 3 Using Specil Right Tringle Architecture The bse of the Msschusetts Institute of Technolog s Building 66, n engineering lbortor, is pproimtel 90 tringle. The length of the hpotenuse of the tringle is bout 294 feet. Find, to the nerest foot, the lengths of the legs of the tringle. 294 ft Solution You need to find the length of the shorter leg first. 2 Find the length of the shorter leg. hpotenuse 2pshorter leg Substitute. Rule for 90 tringle 47 Divide ech side b 2. Find the length of the longer leg. longer leg shorter legp Rule for 90 tringle Substitute. Use clcultor. Answer The length of the shorter leg of the tringle is 47 feet. The length of the longer leg is bout 255 feet. INTERNET 9.6 Eercises eworkbook Plus Guided Prctice More Prctice, p. 8 CLASSZONE.COM Vocbulr Check Skill Check. Ech leg of 90 tringle hs length of 5 units. Wht is the length of the hpotenuse? 2. How is the length of the longer leg of 90 tringle relted to the length of the shorter leg? Find the unknown length. Write our nswer in simplest form Grphic Arts A grphic rtist s tools include tringle. The hpotenuse of the tringle hs length of 0 inches. To the nerest inch, how long re the legs of the tringle? in. Lesson 9.6 Specil Right Tringles 485
4 Pge 4 of 5 Prctice nd Problem Solving Homework Help Emple Eercises 7 9, 4, , , 5 Online Resources CLASSZONE.COM More Emples etutoril Plus Find the unknown lengths. Write our nswers in simplest form Spekers You connect stereo sstem to our television set. The directions s tht the spekers should be in line with our television nd 2 feet prt s shown.. Find the distnce between ou nd the television set to the nerest foot. b. Find the distnce between ou nd ech speker to the nerest foot. 4. Writing Eplin wh n two 90 tringles re similr. 5. Softbll The bses on softbll field form squre with side length of 60 feet. You throw softbll from first bse to third bse. How fr do ou throw the softbll? Round our nswer to the nerest foot. You 5 60 ft 3rd 2nd Speker TV Speker 60 ft st 2 2 ft Find the unknown lengths. Write our nswers in simplest form Etended Problem Solving There is prk in our town tht is squre with side length of 800 feet. You pln to wlk from one corner of the squre to the opposite corner.. Compre To the nerest foot, how much shorter is the distnce from one corner to the opposite corner long the digonl thn the distnce long two sides of the squre? b. You wlk t rte of 3 miles per hour. Find our rte in feet per second. c. Interpret To the nerest second, how much time would ou sve b wlking long the digonl rther thn wlking long two sides of the squre? 486 Chpter 9 Rel Numbers nd Right Tringles
5 Pge 5 of Wrenches You must choose the right size wrench to tighten nut. Ech edge of the nut hs length of 4 inch. You should choose wrench size tht is close to the distnce cross the nut from one edge to the opposite edge. Which wrench size should ou use, 3 8 inch, 7 inch, or 6 2 inch? 4 4 in. in. 2. Chllenge Find the vlue of. Give our nswer s rdicl in simplest form. 0 3 Mied Review Solve the proportion. (Lesson 6.2) 22. w z Submrines A silor on submrine uses periscope to view the surfce of the ocen. The periscope s height h (in feet) bove the surfce nd the distnce d (in miles) tht the silor cn see re relted 2 d b the formul h. Suppose the periscope is t height of 3 feet.. 4 To the nerest mile, how fr cn the silor see? (Lesson 9.) Find the midpoint of the segment with the given endpoints. (Lesson 9.5) 27. ( 3, 4), (, 6) 28. (8, 3), ( 2, 7) 29. (4,.), ( 2.4,.7) Stndrdized Test Prctice 30. Multiple Choice Wht is the vlue of? 2 A. ft B. 2 ft 3 C. 2 3 ft D ft 24 ft 3. Multiple Choice Ech leg of 90 tringle hs length of 5 units. Wht is the length of the hpotenuse? 5 F. 7.5 units G. units H. 5 units I. 5 2 units Short Response Eplin how to find the re of the equilterl tringle shown. 8 Lesson 9.6 Specil Right Tringles 487
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