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Name: ________________________ Class: ___________________ Date: __________ ID: A Geometry - Chapter 8 Corrective #1 1516 Matching Match each vocabulary term with its definition. a. cosine b. adjacent leg c. sine d. tangent e. trigonometric ratio f. angle of depression g. opposite leg h. angle of elevation i. geometric mean ____ ____ ____ ____ ____ ____ ____ the angle formed by a horizontal line and a line of sight to a point below in a right triangle, the ratio of the length of the leg opposite the angle to the length of the hypotenuse in a right triangle, the ratio of the length of the leg adjacent to the angle to the length of the hypotenuse a ratio of two sides of a right triangle the angle formed by a horizontal line and a line of sight to a point above a x 6. for positive numbers a and b, the positive number x such that = x b 7. in a right triangle, the ratio of the length of the leg opposite the angle to the length of the leg adjacent to the angle 1. 2. 3. 4. 5. Match each vocabulary term with its definition. a. parallel vectors b. resultant vector c. additive vector d. direction e. equal vectors f. magnitude g. multiplicative vector h. component form i. vector ____ ____ ____ ____ ____ ____ ____ | → | | → | 8. the length of a vector, written | AB | or | v | | | | | 9. the orientation of a vector, which is determined by the angle the vector makes with a horizontal line 10. a quantity that has both magnitude and direction 11. the form of a vector that lists the vertical and horizontal change from the initial point to the terminal point 12. two vectors that have the same magnitude and the same direction 13. the vector that represents the sum of two given vectors 14. vectors with the same or opposite direction 1 Name: ________________________ ID: A Multiple Choice Identify the choice that best completes the statement or answers the question. ____ 15. A pilot flying at an altitude of 1.8 km sights the runway directly in front of her. The angle of depression to the beginning of the runway is 31°. The angle of depression to the end of the runway is 23°. What is the length of the runway? Round to the nearest tenth of a kilometer. a. 1.2 km c. 1.3 km b. 0.9 km d. 1.0 km ____ 16. Identify the parallel vectors and the equal vectors. → a. → → → Parallel: AB , CD , HI , JK → → Equal: AB , CD → b. → → → → Parallel: AB , CD , FG , HI → → Equal: AB , CD → → Parallel: AB , CD , JK → → c. d. → Equal: AB , CD → → Parallel: AB , CD , HI → → → Equal: AB , CD , HI Short Answer 17. A hiking trail has a slope of 3 32 . What is the measure of the angle that the trail makes with a horizontal line? Round to the nearest degree. 2 Name: ________________________ ID: A 18. Draw the vector −2, 2 on the coordinate plane. Find its magnitude to the nearest tenth. → → 19. TM has an initial point of (−2, 8) and a terminal point of (−6, − 4). Find the magnitude of TM to the nearest tenth. . 20. Find the geometric mean of the pair of numbers 4 and 25. 21. Write the trigonometric ratio for cos X as a fraction and as a decimal rounded to the nearest hundredth. 3 Name: ________________________ ID: A Completion Complete each statement. 22. Label the angles and side relationships for the 30-60-90 triangle by filling in the 6 boxes with the correct values/expressions. 23. Label the angles and side relationships for the 45-45-90 triangle by filling in the 6 boxes with the correct values/expressions. 4 ID: A Geometry - Chapter 8 Corrective #1 1516 Answer Section MATCHING 1. 2. 3. 4. 5. 6. 7. ANS: ANS: ANS: ANS: ANS: ANS: ANS: F C A E H I D TOP: TOP: TOP: TOP: TOP: TOP: TOP: 8-4 Angles of Elevation and Depression 8-2 Trigonometric Ratios 8-2 Trigonometric Ratios 8-2 Trigonometric Ratios 8-4 Angles of Elevation and Depression 8-1 Similarity in Right Triangles 8-2 Trigonometric Ratios 8. 9. 10. 11. 12. 13. 14. ANS: ANS: ANS: ANS: ANS: ANS: ANS: F D I H E B A TOP: TOP: TOP: TOP: TOP: TOP: TOP: 8-6 Vectors 8-6 Vectors 8-6 Vectors 8-6 Vectors 8-6 Vectors 8-6 Vectors 8-6 Vectors MULTIPLE CHOICE 15. ANS: A 16. ANS: A TOP: 8-4 Angles of Elevation and Depression TOP: 8-6 Vectors SHORT ANSWER 17. ANS: 5 TOP: 8-3 Solving Right Triangles 1 ID: A 18. ANS: 6.7 TOP: 8-6 Vectors 19. ANS: 12.6 TOP: 8-6 Vectors 20. ANS: 10 TOP: 8-1 Similarity in Right Triangles 21. ANS: 12 cos X = = 0.80 15 TOP: 8-2 Trigonometric Ratios COMPLETION 22. ANS: TBD 23. ANS: TBD 2