Chapter 7 Test. 6. Choose the set that is the possible side lengths of a right triangle. a. 1, 1, 2 c. 3, 4, 7 b. 1, 3, 2 d.
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1 Chapter 7 Test 1. How long is a string reahing from the top of a 9-ft pole to a point on the ground that is 7 ft from the ase of the pole? a. 120 ft. 42 ft. 32 ft d. 130 ft 2. A radio station is going to onstrut a 5-foot tower on top of a uilding. The tower will e supported y three ales, eah attahed to the top of the tower and to points on the roof of the uilding that are 12 feet from the ase of the tower. Find the total length of the three ales. a. 13 ft. 52 ft. 39 ft d. 65 ft 3. Whih set of lengths annot form a right triangle? a. 6 mm, 8 mm, 10 mm. 3 mm, 4 mm, 5 mm. 1.5 mm, 2 mm, 2.5 mm d. 4 mm, 4 mm, 5 mm 4. A ship in alm seas steamed 12 km in one diretion, turned and steamed 12 km in another diretion, and then returned 8 km ak to its original position. The aptain then plotted the ship's ourse on a nautial hart. She asked her first offier to look at the hart and desrie the ship's path. Did the first offier desrie it as an aute, otuse, or right triangle? Then the seond offier said she ould further identify whether the path was salene, isoseles, or equilateral. What did she determine? a. otuse; salene. aute; salene. aute; equilateral d. aute; isoseles 5. Li went for a mountain-ike ride in a relatively flat, wooded area. She rode for 4 km in one diretion, then turned and peddled 7 km in another. Finally she turned and rode 5 km in yet another diretion. Stopping, Li took out a map and drew her path. Could Li e ak at her starting point? Could her path e a right triangle? a. Yes; Yes. No; No. Yes; No d. No; Yes 6. Choose the set that is the possile side lengths of a right triangle. a. 1, 1, 2. 3, 4, 7. 1, 3, 2 d. 3, 5, 9
2 7. For eah set of numers, determine whether the numers represent the lengths of the sides of an aute triangle, a right triangle, an otuse triangle, or no triangle. a. 50, 28, 22. 8, 10, , 9.6, Solve for a and. 9. Find a,, and h. 10. Given: ΔACD is a right triangle; DB is an altitude of ΔACD; BE is an altitude of ΔADB Prove: ΔABE ΔDCB 11. The shorter leg of a triangle is 8.6 feet long. Find the perimeter. a. Ê ˆ Ë Á ft. Ê ˆ Ë Á ft
3 . Ê ˆ Ë Á ft d. Ê ˆ Ë Á ft 12. Find the value of x and y. 13. What is the length of the diagonal of a square with side lengths 7 2? 14. Find the value of x and y. 15. Find tan B for the right triangle elow: Use a speial right triangle to find the tangent of the given angle. 17. Write os B.
4 a d Use the diagram to find sin x as a fration in simplest form. a d Find tan B for the right triangle elow: a d Find sin P, os P, tan P.
5 1. = _ = _ 3. = _ 4. = _ a = _ 6. = _ 7. a = _ 8. = _ = _ = _ 11. = _ 12. = = _ 14. = _ 15. = _ = 35 There is a slide in the park that is 18 feet long. The ladder to the top of the slide is 7.5 feet long. If the ladder and the slide are perpendiular, what is d, the distane from the top of the slide to the ground?
6
7 Chapter 7 Test Answer Setion 1. ANS: D PTS: 1 DIF: Level B REF: MGEO0018 TOP: Lesson 7.1 Apply the Pythagorean Theorem KEY: solve word right triangles Pythagorean Theorem BLM: Appliation 2. ANS: B PTS: 1 DIF: Level B REF: MGEO0019 NAT: NCTM 9-12.PRS.2 STA: AK.AKGLE.MTH PS-5 TOP: Lesson 7.1 Apply the Pythagorean Theorem KEY: word Pythagorean Theorem BLM: Appliation 3. ANS: D PTS: 1 DIF: Level B REF: DITT0026 NAT: NCTM 9-12.GEO.1.a KEY: right triangles Pythagorean Theorem onverse BLM: Knowledge 4. ANS: D PTS: 1 DIF: Level B REF: BMGM0291 NAT: NCTM 9-12.GEO.1.a KEY: word lassifying triangles BLM: Knowledge 5. ANS: B PTS: 1 DIF: Level B REF: MGEO0020 NAT: NCTM 9-12.GEO.1.a NCTM 9-12.PRS.2 STA: AK.AKGLE.MTH PS-5 KEY: word lassifying triangles right triangles BLM: Comprehension 6. ANS: B PTS: 1 DIF: Level B REF: MLGE0156 KEY: right triangles Pythagorean Theorem onverse BLM: Knowledge 7. ANS: a. right triangle,. otuse triangle,. no triangle PTS: 1 DIF: Level B REF: MLGE0159 NAT: NCTM 9-12.GEO.1.a KEY: lassifying triangles BLM: Knowledge 8. ANS: a = 63; = 105 PTS: 1 DIF: Level B REF: MLGE0424 NAT: NCTM 9-12.GEO.1.d STA: AK.AKGLE.MTH MEA-2 TOP: Lesson 7.3 Use Similar Right Triangles KEY: similar right triangles geometri mean BLM: Knowledge 9. ANS: a = 10, = 10 3, h = 5 3 PTS: 1 DIF: Level B REF: SXAM0042 NAT: NCTM 9-12.GEO.1. TOP: Lesson 7.3 Use Similar Right Triangles
8 KEY: similar right triangles geometri mean 10. ANS: Statements Reasons ΔACD is a right triangle DB is an altitude of ΔACD ΔADB ΔDCB BE is an altitude of ΔADB ΔABE ΔADB ΔABE ΔDCB Given. Given. If the altitude is drawn to the hypotenuse of a right triangle, then the two triangles formed are similiar to eah other. Given. If the altitude is drawn to the hypotenuse of a right triangle, then the two triangles formed are similiar to the original triangle. Transitive Property BLM: Knowledge PTS: 1 DIF: Level B REF: GE PF.04 NAT: NCTM 9-12.REA.4 NCTM 9-12.GEO.1. NCTM 9-12.REA.3 STA: AK.AKGLE.MTH PS-4 TOP: Lesson 7.3 Use Similar Right Triangles KEY: proof similar right triangles geometri mean BLM: Evaluation 11. ANS: A PTS: 1 DIF: Level B REF: DBXM1015 TOP: Lesson 7.4 Speial Right Triangles KEY: speial right triangles triangle BLM: Comprehension 12. ANS: x = 15 2, y = or 15(1 + 3) PTS: 1 DIF: Level A REF: AGEO0706 NAT: NCTM 9-12.GEO.1.a TOP: Lesson 7.4 Speial Right Triangles KEY: speial right triangles triangle triangle BLM: Knowledge 13. ANS: 14 PTS: 1 DIF: Level B REF: MLGE0161 TOP: Lesson 7.4 Speial Right Triangles KEY: speial right triangles triangle BLM: Comprehension 14. ANS: x = 15, y = 15 3 PTS: 1 DIF: Level A REF: GGEO0804 TOP: Lesson 7.4 Speial Right Triangles KEY: speial right triangles triangle BLM: Knowledge 15. ANS:
9 12 5 PTS: 1 DIF: Level A REF: MLGM0046 STA: AK.AKGLE.MTH MEA-2 TOP: Lesson 7.5 Apply the Tangent Ratio KEY: tangent ratio BLM: Knowledge 16. ANS: 3 PTS: 1 DIF: Level B REF: 7f4a77-d-11d f7 TOP: Lesson 7.5 Apply the Tangent Ratio KEY: speial right triangle tangent ratio BLM: Knowledge 17. ANS: B PTS: 1 DIF: Level A REF: MHGM0136 STA: AK.AKGLE.MTH MEA-2 TOP: Lesson 7.6 Apply the Sine and Cosine Ratios KEY: sine and osine ratios trigonometri ratios BLM: Knowledge 18. ANS: B PTS: 1 DIF: Level B REF: PMG80821 STA: AK.AKGLE.MTH MEA-2 TOP: Lesson 7.6 Apply the Sine and Cosine Ratios KEY: trigonometri ratios sine and osine ratios BLM: Knowledge 19. ANS: B PTS: 1 DIF: Level B REF: XEA21403 STA: AK.AKGLE.MTH MEA-2 TOP: Lesson 7.6 Apply the Sine and Cosine Ratios KEY: trigonometri ratios sine and osine ratios tangent ratio BLM: Knowledge 20. ANS: sin P = 9, os P = , tan P = 9 40 PTS: 1 DIF: Level B REF: GGEO0805 STA: AK.AKGLE.MTH MEA-2 TOP: Lesson 7.6 Apply the Sine and Cosine Ratios KEY: sine and osine ratios tangent ratio trigonometri ratios BLM: Knowledge
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