Geometry: Chapter 7. Name: Class: Date: 1. Find the length of the leg of this right triangle. Give an approximation to 3 decimal places.

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1 Name: Class: Date: Geometry: Chapter 7 1. Find the length of the leg of this right triangle. Give an approximation to 3 decimal places. a c b d ABC is a right triangle. AB = _. a c. 3 5 b. 3 6 d If a, b, and c are sides of a right triangle, which of the following are also sides of a right triangle? a. The square root of each length ( a, b, c ) b. Twice the length of each side (2a, 2b, 2c) c. Four more than each length (a + 4, b + 4, c + 4) d. The square of each length 4. Which of the following sets of numbers is a Pythagorean triple? 1 a. 3, 4, 5 c. 3, 1 4, 1 5 b. 12, 16, 20 d. 3 2, 4 2, A set of Pythagorean triples is _. a. 3, 5, 9 c. 6, 9, 12 b. 1, 1, 2 d. 5, 12, 13 1

2 Name: 6. A 25.5 foot ladder rests against the side of a house at a point 24.1 feet above the ground. The foot of the ladder is x feet from the house. Find the value of x to one decimal place. a. 1.9 b. 7.0 c. 8.3 d GRIDDED RESPONSE Grid the correct answer on a separate gridding sheet. A power pole broke and fell as shown. To the nearest tenth of a meter, what was the original height of the pole? 8. Which set of lengths cannot form a right triangle? a. 6 mm, 12 mm, 13 mm c. 2.5 mm, 6 mm, 6.5 mm b. 5 mm, 12 mm, 13 mm d. 10 mm, 24 mm, 26 mm 9. If the side lengths of a triangle are 7, 6, and 9, the triangle _. a. is an obtuse triangle c. is an acute triangle b. is a right triangle d. cannot be formed 10. A ship in calm seas steamed 12 km in one direction, turned and steamed 12 km in another direction, and then returned 8 km back to its original position. The captain then plotted the ship's course on a nautical chart. She asked her first officer to look at the chart and describe the ship's path. Did the first officer describe it as an acute, obtuse, or right triangle? Then the second officer said she could further identify whether the path was scalene, isosceles, or equilateral. What did she determine? a. acute; scalene c. acute; isosceles b. acute; equilateral d. obtuse; scalene 2

3 Name: 11. Mark went for a mountain-bike ride in a relatively flat, wooded area. He rode for 7 km in one direction, then turned and peddled 5 km in another. Finally he turned and rode 7 km in yet another direction. Stopping, Mark took out a map and drew his path. Could Mark be back at his starting point? Could his path be a right triangle? a. Yes; Yes c. No; Yes b. No; No d. Yes; No 12. Choose the set that is the possible side lengths of a right triangle. a. 1, 1, 2 c. 3, 4, 7 b. 1, 1, 2 d. 3, 5, Choose the set that is the possible side lengths of a right triangle. a. 4, 9, 13 c. 1, 1, 2 b. 2, 2, 2 d. 8, 15, GRIDDED RESPONSE Grid the correct answer on a separate gridding sheet. The diagonals of a picture frame do not have the same length because its loose joints are not forming right angles. To make the corners of the picture frame form right angles, a wire is fastened to one corner of the frame on the longer diagonal. Then it is drawn across to the opposite corner and tightened until the frame is rectangular. The frame is supposed to be 16 inches wide and 36 inches tall. To the nearest hundredth of an inch, how long is the diagonal of the frame when its corners are square? 15. A triangle has side lengths of 7, 9, and 11. Decide whether it is an acute, right, or obtuse triangle. 16. Find a, b, and h. 17. Find the length of the altitude drawn to the hypotenuse. 18. In a triangle, the ratio of the length of the hypotenuse to the length of a side is _. a. 1:1 b. 3:1 c. 2:1 d. 2:1 3

4 Name: 19. Which of the following cannot be the lengths of a triangle? 21 a. 13, 42 13, 21 3 c. 27, 54, b. 23, 46, 46 3 d. 6, 12, An equilateral triangle has side lengths of 10. The length of its altitude is _. a b. 5 c d In a triangle, the ratio of the length of the hypotenuse to the length of the shorter side is _. a. 2: 3 b. 2:1 c. 2:1 d. 3:1 22. A photographer shines a camera light at a particular painting forming an angle of 40 with the camera platform. If the light is 58 feet from the wall where the painting hangs, how high above the platform is the painting? a ft b ft c ft d ft 23. A tree 19 feet tall casts a shadow which forms an angle of 49 with the ground. How long is the shadow to the nearest hundredth? 24. Write cos B. a b c d

5 Name: 25. Use your calculator to find cos 23. a. about c. about 1.07 b. about d. about To find the height of a tower, a surveyor positions a transit that is 2 meters tall at a spot 95 meters from the base of the tower. She measures the angle of elevation to the top of the tower to be 32. What is the height of the tower, to the nearest meter? a. 154 m b. 59 m c. 61 m d. 152 m 27. Liola drives 16 km up a hill that is at a grade of 10 o. What horizontal distance, to the nearest tenth of kilometer, has she covered? a km b km c km d km 28. What is x to the nearest hundredth? (not drawn to scale) a. x = b. x = c. x = d. x = Find tan B for the right triangle below: a b c d Find the missing angle and side measures of ABC, given that m A = 65, m C = 90, and CB = 15. a. m B = 25, c = 16.6, b = 7 b. m B = 155, c = 16.6, b = 7.5 c. m B = 155, c = 16.6, b = 7 d. m B = 25, c = 16.1, b = Two legs of a right triangle have lengths 15 and 8. The measure of the smaller acute angle is _. a b. 17 c d

6 Name: 32. Which of the following is NOT enough information to solve a right triangle? a. Two sides b. One side length and one trigonometric ratio c. Two angles d. One side length and one acute angle measure 33. Assume that A is an acute angle. If sin A = , find tan A to four decimal places. (Use your calculator.) 34. An antenna is atop the roof of a 100-foot building, 10 feet from the edge, as shown in the figure below. From a point 50 feet from the base of the building, the angle from ground level to the top of the antenna is 66. Find x, the height of the antenna, to the nearest foot. Find the measure of an acute angle that satisfies the given equation. Round your answers to the nearest tenth of a degree. 35. cos Z =

7 Geometry: Chapter 7 Answer Section 1. ANS: A PTS: 1 DIF: Level A REF: MLGE0378 STA: MI.MIGLC.MTH L1.1.6 MI.MIGLC.MTH G1.2.3 MI.MIGLC.MTH G1.3.1 TOP: Lesson 7.1 Apply the Pythagorean Theorem KEY: Pythagorean Theorem right triangles 2. ANS: A PTS: 1 DIF: Level B REF: HLGM0696 STA: MI.MIGLC.MTH L1.1.6 MI.MIGLC.MTH G1.2.3 MI.MIGLC.MTH G1.3.1 TOP: Lesson 7.1 Apply the Pythagorean Theorem KEY: right triangles Pythagorean Theorem 3. ANS: B PTS: 1 DIF: Level B REF: HLGM0707 NAT: NCTM 9-12.GEO.1.b STA: MI.MIGLC.MTH G2.3.3 TOP: Lesson 7.1 Apply the Pythagorean Theorem KEY: right triangles Pythagorean Theorem 4. ANS: B PTS: 1 DIF: Level B REF: MLGE0158 STA: MI.MIGLC.MTH G1.2.3 TOP: Lesson 7.1 Apply the Pythagorean Theorem KEY: Pythagorean triples Pythagorean Theorem 5. ANS: D PTS: 1 DIF: Level B REF: HLGM0701 STA: MI.MIGLC.MTH G1.2.3 TOP: Lesson 7.1 Apply the Pythagorean Theorem KEY: Pythagorean triples Pythagorean Theorem 6. ANS: C PTS: 1 DIF: Level A REF: HLGM0704 NAT: NCTM 9-12.PRS.2 STA: MI.MIGLC.MTH L1.1.6 MI.MIGLC.MTH G1.2.3 MI.MIGLC.MTH G1.3.1 TOP: Lesson 7.1 Apply the Pythagorean Theorem KEY: right triangles Pythagorean Theorem BLM: Application 7. ANS: 20.0 PTS: 1 DIF: Level A REF: MC NAT: NCTM 9-12.PRS.2 NCTM 9-12.REP.1 STA: MI.MIGLC.MTH L1.1.6 MI.MIGLC.MTH L2.3.2 MI.MIGLC.MTH G1.2.3 MI.MIGLC.MTH G1.3.1 TOP: Lesson 7.1 Apply the Pythagorean Theorem KEY: word right triangles Pythagorean Theorem 8. ANS: A PTS: 1 DIF: Level B REF: DITT0026 STA: MI.MIGLC.MTH G1.2.3 KEY: right triangles Pythagorean Theorem converse 1

8 9. ANS: C PTS: 1 DIF: Level B REF: HLGM0713 STA: MI.MIGLC.MTH G1.2.2 MI.MIGLC.MTH G1.2.3 MI.MIGLC.MTH G1.3.1 KEY: classifying triangles 10. ANS: C PTS: 1 DIF: Level B REF: BMGM0291 STA: MI.MIGLC.MTH G1.2.2 KEY: word classifying triangles 11. ANS: D PTS: 1 DIF: Level B REF: MGEO0020 NCTM 9-12.PRS.2 STA: MI.MIGLC.MTH G1.2.3 MI.MIGLC.MTH G1.3.1 KEY: word classifying triangles right triangles BLM: Comprehension 12. ANS: B PTS: 1 DIF: Level B REF: MLGE0156 STA: MI.MIGLC.MTH G1.2.3 MI.MIGLC.MTH G1.3.1 KEY: right triangles Pythagorean Theorem converse 13. ANS: B PTS: 1 DIF: Level B REF: MLGE0157 STA: MI.MIGLC.MTH G1.2.3 MI.MIGLC.MTH G1.3.1 KEY: right triangles sides Pythagorean Theorem converse 14. ANS: PTS: 1 DIF: Level B REF: MC NAT: NCTM 9-12.REP.1 NCTM 9-12.PRS.2 STA: MI.MIGLC.MTH L1.1.6 MI.MIGLC.MTH L2.3.2 MI.MIGLC.MTH G1.2.3 MI.MIGLC.MTH G1.3.1 KEY: word right triangles Pythagorean Theorem 15. ANS: It is an acute triangle. PTS: 1 DIF: Level B REF: HLGM0714 STA: MI.MIGLC.MTH G1.2.2 MI.MIGLC.MTH G1.2.3 MI.MIGLC.MTH G1.3.1 KEY: classifying triangles 2

9 16. ANS: a = 12, b = 24 2, h = 8 2 PTS: 1 DIF: Level B REF: SXAM0042 NAT: NCTM 9-12.GEO.1.b STA: MI.MIGLC.MTH L1.1.6 MI.MIGLC.MTH G1.2.3 MI.MIGLC.MTH G1.3.1 TOP: Lesson 7.3 Use Similar Right Triangles KEY: similar right triangles geometric mean 17. ANS: 6 PTS: 1 DIF: Level B REF: BMGM0300 TOP: Lesson 7.3 Use Similar Right Triangles KEY: similar right triangles geometric mean 18. ANS: C PTS: 1 DIF: Level A REF: HLGM0728 STA: MI.MIGLC.MTH L1.1.6 MI.MIGLC.MTH G1.2.4 TOP: Lesson 7.4 Special Right Triangles KEY: special right triangles triangle 19. ANS: B PTS: 1 DIF: Level B REF: PHGM0523 STA: MI.MIGLC.MTH L1.1.6 MI.MIGLC.MTH G1.2.4 TOP: Lesson 7.4 Special Right Triangles KEY: special right triangles triangle 20. ANS: D PTS: 1 DIF: Level B REF: HLGM0725 STA: MI.MIGLC.MTH L1.1.6 MI.MIGLC.MTH A3.7.3 MI.MIGLC.MTH G1.2.4 MI.MIGLC.MTH G1.2.5 MI.MIGLC.MTH G1.3.1 MI.MIGLC.MTH G1.3.3 TOP: Lesson 7.4 Special Right Triangles KEY: equilateral triangle altitude triangle BLM: Comprehension 21. ANS: C PTS: 1 DIF: Level B REF: HLGM0729 STA: MI.MIGLC.MTH L1.1.6 MI.MIGLC.MTH G1.2.4 TOP: Lesson 7.4 Special Right Triangles KEY: triangle 22. ANS: B PTS: 1 DIF: Level B REF: PMG80819 NAT: NCTM 9-12.GEO.1.d NCTM 9-12.PRS.2 TOP: Lesson 7.5 Apply the Tangent Ratio KEY: word tangent ratio BLM: Application 3

10 23. ANS: ft PTS: 1 DIF: Level A REF: PMG80820 NAT: NCTM 9-12.PRS.2 NCTM 9-12.GEO.1.d TOP: Lesson 7.5 Apply the Tangent Ratio KEY: word tangent ratio BLM: Application 24. ANS: B PTS: 1 DIF: Level A REF: MHGM0136 KEY: sine and cosine ratios trigonometric ratios 25. ANS: A PTS: 1 DIF: Level A REF: HLGM0741 NAT: NCTM 9-12.NOP.3.a KEY: sine and cosine ratios calculator 26. ANS: C PTS: 1 DIF: Level B REF: MHGM0095 NAT: NCTM 9-12.GEO.1.d NCTM 9-12.PRS.2 KEY: word trigonometric ratios sine and cosine ratios tangent ratio BLM: Application 27. ANS: C PTS: 1 DIF: Level A REF: PHGM1134 NAT: NCTM 9-12.GEO.1.d NCTM 9-12.PRS.2 KEY: word trigonometric ratios sine and cosine ratios 28. ANS: D PTS: 1 DIF: Level A REF: MLGE0381 NAT: NCTM 9-12.GEO.1.d KEY: sine and cosine ratios 29. ANS: D PTS: 1 DIF: Level B REF: XEA21403 KEY: trigonometric ratios sine and cosine ratios tangent ratio 30. ANS: A PTS: 1 DIF: Level B REF: MHA10127 NAT: NCTM 9-12.GEO.1.d STA: MI.MIGLC.MTH G1.2.1 MI.MIGLC.MTH G1.2.2 MI.MIGLC.MTH G1.3.1 MI.MIGLC.MTH G1.3.3 TOP: Lesson 7.7 Solve Right Triangles KEY: solving right triangles sine and cosine ratios 4

11 31. ANS: D PTS: 1 DIF: Level B REF: HLGM0749 NAT: NCTM 9-12.GEO.1.d TOP: Lesson 7.7 Solve Right Triangles KEY: solving right triangles 32. ANS: C PTS: 1 DIF: Level B REF: HLGM0752 TOP: Lesson 7.7 Solve Right Triangles KEY: solving right triangles BLM: Comprehension 33. ANS: PTS: 1 DIF: Level B REF: HLGM0744 NAT: NCTM 9-12.NOP.3.a NCTM 9-12.GEO.1.d TOP: Lesson 7.7 Solve Right Triangles KEY: inverse sine tangent ratio 34. ANS: x 35 ft PTS: 1 DIF: Level B REF: MGEO0022 NAT: NCTM 9-12.GEO.1.b STA: MI.MIGLC.MTH L1.1.6 MI.MIGLC.MTH G1.2.3 MI.MIGLC.MTH G1.3.1 MI.MIGLC.MTH G2.3.3 MI.MIGLC.MTH G2.3.4 TOP: Lesson 7.7 Solve Right Triangles KEY: word solving right triangles similar right triangles sine and cosine ratios BLM: Application 35. ANS: m Z 67.4 PTS: 1 DIF: Level A REF: BS NAT: NCTM 9-12.GEO.1.d TOP: Lesson 7.7 Solve Right Triangles KEY: inverse cosine 5

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