Geometry Chapter 9 Practice Test Answers

h Ml NAME TESTE Geometry - Chp 9 Practice Test 1. A castle guard is standing on the opposite side of a 4 -foot moat and wants to reach a window that is 28 feet above the ground. The guard props a ladder against the castle wall to form a right triangle as shown. Approximate the length of the ladder needed to reach the window to the nearest tenth of a foot. 1 - I I + 1SK llr $00 28 ft I ^ 800 I X NC r. * 'f - ~ I Not drawn to scale ^ c. about 27.7 ft a ) about 28.3 ft E 32.0 ft d. 800.0 ft 2. An adventure company wants to run a zip line from the top of one building that is 95 feet tall to the top of another building that is 40 feet tall. The two buildings are 76 feet apart. Estimate the length (in feet) of the zip line. Round your 4. In the diagram, AC = 6 . Find AB. Write your answer in simplest form. answer to the nearest tenth. a . about 52.4 ft C. 25° l yi b. about 131.0 ft about 55.0 ft 1 Le / oN about 93.8 ft JisoT HO V 3. Determine whether segments with lengths of 16, 30, and 34 form a triangle. If so, classify the triangle as acute, right, or obtuse. a . not a triangle b. obtuse triangle c. acute triangle 9 ^^ right triangle a. AB = 6 He 4 3 D > 7 2 ^ "1 " l o * St) ' n$ u b. = fu ( c) AB d . AB . c i -- ^ AB = 3 12 2 r Geometry - Chp 9 Practice Test TESTE 5. In the diagram, AB = 54. Find ylC and BC. Write your answers in simplest form. 7. Gym members are instructed to lift their legs at a 60° angle during leg lifts. One member has legs that are 28 inches long. What is the height (in inches) of the member’s feet during the leg lift? If necessary, round decimal answers to the nearest tenth. a. about 9.3 in. about 24.2 in. c . about 19.8 in. d . about 14.0 in. B C ml V JI Find the exact value of the variable. A (J) AC = 21\[T , BC = 27 b. AC = 27, BC = 27 ”\/7 8. ' c. AC = 18, BC = 36 d . AC = 3 6, BC = 1 8 6. A chemistry teacher makes a sign for the door to the room that contains the chemicals used in class. The danger sign is shaped like an equilateral triangle. Estimate the area of the sign to the nearest tenth of a square inch . 72 x a. x = 576 ~ b. x = 8 j85 16 y:1 * * \% L Jlltr U * ) x = 24 VF d. x - 2 \] 22 ~ y - J s i le - Z b a. about 54.0 in. 2 ( b ) about 140.3 in.2 c. about 70.1 in. 2 2 d . about 280.6 in. . *!. 2 Geometry - Chp 9 Practice Test TESTE . Find the value(s) of the variable(s) If necessary, round decimal answers to the nearest tenth. A1 ^ 9. <2 <5 WH y 4 11 . s 12 * 2 i 8 a. x ** 5.7 b. x » 6.0 ' a . y = 4 '\/ l 3 b. y = 4 "\[(i x x CL § v == 48 18 y ~ 7.0 ~ 6.7 12 . 10. A* X 5 * . y. ^ ( j ) 9 w a. b. x *> iox * S - W 37.3 11.7 6.2 19.7 ' - " a. w = 3 v/ l 4 © c. d. - ^Vl w 70 w= ?" w=3 lO VO 13. 49 iM “ * 34 o y *- H °[ s ^7> M * -- 21- H Vs a. x » 59.1, y » 87.6 b. x » 40.6, » 27.4 . Ml ©d x ® 27.4, y » 40.6 . x « 87.6 , » 59.1 i 'f - M O 3 1 U r Geometry - Chp 9 Practice Test TESTE Vfl . * t 16. Use a special right triangle to find the tangent of a 60 ° angle. 14. y i: lV l? (a) IS to $ U a . x « 18.3 , y « 3.5 ®' x « 3.5 , y * 18.3 c. x =* 94.3, 92.6 « « d . x 92.6, jy 94.3 i* l 3 , 1 <6 1 * a. Vi b. 2 VT d. - iS - V 2 c. dL 3 d. 1 2 r /l to ® a. i'ftft 2° n V2 " \ I dL 2 •L, ^ d. 2 1 2 18. A car is traveling along a road that makes a 10° angle with the ground. Find the elevation of the car on a stretch of road that extends horizontally 97 meters. Round your answer to the nearest tenth . .- lo ^c * , r. Not drawn to scale c. about 550.1 m d. about 149.6 m 4 ^ ' :1 [ VT about 17.1 m about 62.9 m Ito “ 17. Use a special right triangle to find the tangent of a 45° angle. ' 15. Use a special right triangle to find the tangent of a 30° angle. " *WN 6 * .JL b. 2 li ( VT • — v: n l ^ rf ZT Geometry - Chp 9 Practice Test po 19. A parasailer is attached to a boat with a rope. While parasailing , the angle of depression to the boat is 23°. When the parasailer is 170 feet above the boat, how long is the rope? Round our answer to the nearest tenth of a foot. ^ aj TESTE * 23. Use a special triangle to find the cosine of a 30° angle. u , about 97.7 ft c, about 184.7 ft d. about 230.1 ft * r V3 no b. - angle. b. d. V7 & * 2 V7 d. ^ 1 p *Z T a a. Z c. angle. To T. -1 d. 2 2 , * 6 Z 2 a :£ 3 I 1 2 . Solve the triangle . Round decimal answers to the nearest tenth . H 6 F- 2 c. tr Z angle. 21 . Use a special triangle to find the sine of a 30° 3 Si 1 2 ± „ 3 2 a. o 24. Use a special triangle to find the sine of a 60° o \ * c. 20 . Use a special triangle to find the sine of a 45° a. t o $ To 2 about 435.1 ft :£ 2 25. * - f - 4^ 1 - 11.9' 11 7 22. Use a special triangle to find the cosine of a 45° angle. a. ^ 2 d. Vi VI 1 2 - <*V .- S 'IA. Z.'ZT s ^U* i I/O VA X l %oo ZSoD ++ & f X ' -- 1« OOS ' ^1 1° * I3 Z 7 . 4 about 2657.0 ft about 1327.4 ft 30. You plan to install a sprinkler system in your yard. You designate one sprinkler head to lie on a vertex of a triangular- gardep with dimensions of 2 5 feet, 12 feet , and 21 feet. The sprinkler heads are ordered according , to the angle through which they rotate. What is the largest angle of rotation you can order? . 5 7° C . 29° 9 5° d. 152° zs - -. i a- x + z i a 7 - L& It s y. ,6 1 Z% ' Z l1 X .X - Z ^ ' \' L - T A '1- ') - ~L AOt *- ' x X - - /zrVi'- n 60 S I - Z A Z) (7 l ) ° '1 ID: E Geometry - Chp 9 Practice Test Answer Section 1. ANS: NAT: NOT: 2. ANS: NAT: NOT: 3. ANS: NAT: KEY: NOT : 4. ANS: NAT : NOT : 5. ANS: NAT: NOT : 6. ANS: NAT : NOT: 7. ANS: NAT: NOT : 8 . ANS: NAT : NOT : 9. ANS: NAT : NOT : 10. ANS: NAT : NOT : 11. ANS: NAT: 12. ANS: NAT: 13. ANS: NAT: NOT: 14 , ANS: NAT: NOT : 15. ANS: NAT: 16. ANS: NAT: A PTS : 1 REF: Geometry Sec. 9.1 DIF : Level 1 HSG-SRT.C.8 KEY : Pythagorean Theorem | application Example 3- 1 D PTS : 1 DIF : Level 2 REF: Geometry Sec. 9.1 HSG-SRT.C.8 KEY : Pythagorean Theorem | application Example 3-2 D PTS : 1 DIF : Level 1 REF: Geometry Sec. 9.1 HSG-SRT.C.8 Triangle Inequality Theorem | Pythagorean Inequalities Theorem Example 5 C PTS : 1 REF: Geometry Sec. 9.2 DIF: Level 1 HSG-SRT.C.8 KEY : special right triangles Example 1 PTS : 1 DIF : Level 1 REF: Geometry Sec. 9.2 A HSG-SRT.C.8 KEY: special right triangles Example 2 PTS : 1 B DIF : Level 2 REF: Geometry Sec. 9.2 HSG-SRT.C.8 | HSG-MG.A.1 KEY: special right triangles | application Example 3-2 PTS : 1 DIF : Level 1 REF: Geometry Sec. 9.2 B HSG-SRT.C.8 | HSG-MG.A.1 KEY: special right triangles | application Example 4 PTS : 1 DIF: Level 1 REF: Geometry Sec. 9.3 C : HSG-SRT.B.5 KEY geometric mean Example 4 C PTS : 1 DIF: Level 1 REF: Geometry Sec. 9.3 HSG-SRT.B.5 KEY : geometric mean Example 4 PTS : 1 B DIF: Level 1 REF: Geometry Sec. 9.3 HSG-SRT. B.5 KEY : geometric mean Example 4 C PTS : 1 . DIF: Level 1 REF: Geometry Sec. 9.4 HSG-SRT.C.6 | HSG-SRT.C.8 NOT : Example 2 KEY: tangent C PTS : 1 DIF: Level 1 REF: Geometry Sec. 9.4 HSG-SRT.C.6 | HSG-SRT.C.8 NOT: Example 2 KEY: tangent C PTS : 1 DIF: Level 1 REF: Geometry Sec. 9.5 HSG-SRT.C.6 | HSG-SRT.C.7 | HSG-SRT.C.8 KEY : sine | cosine Example 3 PTS: 1 B DIF: Level 1 REF: Geometry Sec. 9.5 HSG-SRT.C.6 | HSG-SRT.C.7 | HSG-SRT.C.8 KEY: sine | cosine Example 3 C PTS: 1 DIF : Level 1 REF: Geometry Sec. 9.4 KEY : tangent HSG-SRT.C.6 | HSG-SRT.C.8 NOT: Example 3 PTS: 1 DIF : Level 1 REF: Geometry Sec. 9.4 A HSG-SRT.C.6 | HSG-SRT.C.8 NOT: Example 3 KEY : tangent 1 ID: E 17. ANS: B PTS : 1 DIF: Level 1 REF: Geometry Sec. 9.4 NAT: HSG-SRT.C.61 HSG-SRT.C.8 KEY : tangent NOT : Example 3 18. ANS: A PTS: 1 DIF : Level 1 REF: Geometry Sec. 9.4 NAT: HSG-SRT.C.6 | HSG-SRT.C. 8 KEY : angle of elevation | application NOT: Example 4-1 19. ANS: A PTS : 1 DIF: Level 1 REF: Geometry Sec. 9.5 NAT: HSG-SRT.C.6 | HSG-SRT.C.7 | HSG-SRT.C.8 KEY: sine j cosine | application NOT: Example 6-1 20. ANS: C PTS: 1 DIF: Level 1 REF: Geometry Sec. 9.5 NAT: HSG-SRT.C.6 | HSG-SRT.C.7 | HSG-SRT.C.8 KEY : sine I cosine NOT: Example 4 21 . ANS: D PTS : 1 DIF: Level 1 REF: Geometry Sec. 9.5 | HSG SRT . . C NAT: 6 HSG-SRT.C.7 [ HSG -SRT.C.8 KEY : sine | cosine NOT: Example 4 22. ANS: C PTS : 1 DIF: Level 1 REF : Geometry Sec. 9.5 NAT: HSG-SRT.C.6 | HSG-SRT.C.7 | HSG-SRT.C.8 KEY: sine I cosine NOT : Example 4 23. ANS: A PTS: 1 DIF: Level 1 REF: Geometry Sec. 9.5 NAT: HSG-SRT.C.6 | HSG-SRT.C.7 | HSG-SRT.C.8 KEY: sine I cosine NOT: Example 4 24. ANS: B PTS: 1 DIF : Level 1 REF: Geometry Sec. 9.5 NAT: HSG-SRT.C.6 | HSG-SRT.C.7 | HSG-SRT.C.8 KEY: sine | cosine NOT: Example 4 25. ANS: B PTS: 1 DIF: Level 1 REF: Geometry Sec. 9.6 NAT: HSG-SRT.C.8 KEY: solve a right triangle NOT: Example 3 26. ANS: C PTS: 1 DIF: Level 1 REF: Geometry Sec. 9.6 NAT: HSG-SRT.C.8 KEY : solve a right triangle NOT: Example 4 27. ANS: A PTS: 1 DIF : Level 1 REF: Geometry Sec. 9.6 NAT : HSG-SRT.C.8 | HSG-MG.A.1 | HSG-MG.A.3 KEY: application | inverse trigonometric ratios NOT: Example 5-1 28. ANS: C PTS: 1 DIF: Level 1 REF: Geometry Sec. 9.7 NAT : HSG-SRT.D.9 KEY : area of a triangle NOT : Example 2 29. ANS: D PTS: 1 REF: Geometry Sec. 9.7 DIF: Level 2 NAT: HSG-SRT.D. 10 | HSG-SRT.D.11 | HSG -MG.A.3 KEY : Law of Sines | application NOT: Example 5-2 30. ANS: B PTS : 1 REF: Geometry Sec. 9.7 DIF: Level 2 NAT: HSG-SRT.D.10 | HSG-SRT. D.ll KEY : Law of Cosines | application NOT: Example 8 [ ! i i 2