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______________________________________ __________ NAME 7-1 DATE ____ PERIOD Skills Practice Geometric Mean Find the geometric mean between each pair of numbers. State exact answers and answers to the nearest tenth. 1, 2 and 8 2. 9 and 36 & 4 and 7 4. 5 and 10 5. 2\’2 and 5\/2 6. 3\’5 and 5V5 Find the measure of each altitude. State exact answers and answers to the nearest tenth. 8. 9 . E2H 10. s T G Find x and y. 11. 12. 13. 14. i GIencoe/McGrawHllI 353 Glencoc Geometry — b-c bs — 7/f/1 Io or ttr I:1 rQ1’ 34: ScieS t7 7) g) )O 39 1s ‘I 1 4 Q _________ __________ PERIOD DATE NAME I Study Guide and Intervention (continued) r Special Right Triangles Properties of 300_600_900 Triangles The sides of a 3O06O09O0 right triangle also have a special relationship. Excun pie I In a 3O0.6O09O0 right triangle, show that the hypotenuse is twice the shorter leg and the longer leg is V times the shorter leg. /.MNQ is a 3O06O09O0 right triangle, and the length of the hypotenuse MN is two times the length of the shorter side NQ. Using the Pythagorean Theorem, 2 = (2x) 2 a 2 4X = — 2 X -1 60° M 2x6 1MNP is an equilateral triangle. 1MNQ is a 3O°-6O°-9O right triangle. x\/i Exrnpie 2 In a 30°-60°-90° right triangle, the hypotenuse is 5 centimeters. Find the lengths of the other two sides of the triangle. If the hypotenuse of a 30°-60°-90° right triangle is 5 centimeters, then the length of the shorter leg is half of 5 or 2.5 centimeters. The length of the longer leg is \/ times the length of the shorter leg, or (2.5)(V’) centimeters. Cxertie5 Findxandy. 2. 1. 3. 5. 9J 12 7. The perimeter of an equilateral triangle is 32 centimeters. Find the length of an altitude of the triangle to the nearest tenth of a centimeter. 8. An altitude of an equilateral triangle is 8.3 meters. Find the perimeter of the triangle to the nearest tenth of a meter. © Glencoe/McGraw-HiII 364 Glencoe Geometry _____________________________________ NAME __________ DATE ____ PERIOD I Skills Practice Trigonometry UsetRSTtoflndsinR,cosR,tanR,sinS,cosS,andtanS. Express each ratio as a fraction and as a decimal to the nearest hundredth. 1. r = 16, s = 30, t = 2. r 34 = 10, s = 24, t — = R 26 s Ir MT Use a calculator to find each value. Round to the nearest ten-thousandth. 3. sin 5 4. tan 23 5. cos 61 6. sin 75.8 7. tan 17.3 8. cos 52.9 Use the figure to find each trigonometric ratio. Express answers as a fraction and as a decimal rounded to the nearest ten-thousandth. 9. tan C 10. sin A B 9 A C 11. cos C Find the measure of each acute angle to the nearest tenth of a degree. 12. sin B = 15. tan C = 0.2985 13. tan A = 0.4168 14. cos R = 0.8443 0.3894 16. cos B = 0.7329 17. sinA = 0.1176 Find x. Round to the nearest tenth. AB @ Glencoe/McGraw-HIII AB 371 LU Glencoe Geometry _____ Kuta SoFtware In! mite AI,.ehra I Nan ic Using Trigonometry To Find Lengths Date Find the missing side. kound to the nearest tenth. I) jX 27’ -25 10 3) 10 4) /1 7, /Z30 x 5) 6) — ix 7) 20 V Period 10) 9) /1 19/ 40 31 10 x II) 12) — / / 38 741 9 /20 x x NJ 14) 13) 18 16) 15) 22 / 17) 18) 37 2— __________ Kuii SoI1 are — Name Infinite AIchra I Using Trigonoirietry to Find Angle Measures E)ate Find each angle nicasure to the nearest degree. I) tan A 2.0503 2) cosZO,1219 3) tan Y = 0.6494 4) sin U=0.1746 cos V = 0.62() 6) sin C = 0.2756 Find the measure of the indicated angle to the nearest degree. 7) 19 55/51 /7 9) 1 34 /114 12) II) 29 _1 38 14) 13) A 42 Period C.) / 7 / Un not ne Lu a at t’ ttZ ‘Tad tha Mae f eah nigonoawtz Tc r eLm Ta the aeaeaal tea thaasaadth, a a Tuft Ta I (C ark Lfr%l I 4) td id at ft t Ih alt Name: Period: Date: Score: Solve Right Triangle Worksheet Solve each right triangle described, given the triangle below. Round angle measure to nearest degree and side measures to the nearest tenth. B 1. a=9,Bt49° a C 2. b B=64°,b=19.2 3. A16°,c14 4. a=0.4,c=O.5 5. a=2,b=7 Snivp Rioht Tricnolp W I 1crm A A Date: Score: Name: Period: Law of Sines/Cosines Worksheet measure to nearest degree and side measures angle Round triangle. Solve each 1, A=42°,b=i2Oc=12O c nearest tenth. 2. b=4l,A=33°B=29° 3, A38°B63°,c 15 4. A53°b4O,c=49 Law of Sine/Cosine WS I Eorm A ) t to) iF a nWrl OX I S I 1 ts gI t t I’ I p I r I