Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Name: ________________________ Class: ___________________ Date: __________ Geometry - Chapter 8 Review 1516 Short Answer 1. Write a similarity statement comparing the three triangles in the diagram. 2. Find sin ∠A to the nearest hundredth. 3. The coordinates of the vertices of ∆RPQ are R(2,−1), P(2,2), and Q(−2,−1) . Find m∠P . 1 ID: A Name: ________________________ ID: A 4. To estimate the height of a radio tower, Jody steps 25 feet away from the center of the tower’s base, until his line of sight to the top of the tower and his line of sight to the center of its base form a right angle. His eyes are 6 feet above the ground. How tall is the radio tower to the nearest foot? 5. Find two angles that satisfy the equation sin(4x + 14)° = cos(–3x + 73)°. → 6. Write the vector AB in component form. 7. The largest Egyptian pyramid is 146.2 m high. When Rowena stands far away from the pyramid, her line of sight to the top of the pyramid forms an angle of elevation of 20° with the ground. What is the horizontal distance between the center of the pyramid and Rowena? Round to the nearest meter. 2 Name: ________________________ ID: A Completion Complete each statement. 8. Label the angles and side relationships for the 30-60-90 triangle by filling in the 6 boxes with the correct values/expressions. 9. Label the angles and side relationships for the 45-45-90 triangle by filling in the 6 boxes with the correct values/expressions. 3 Name: ________________________ ID: A 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 ____ 10. the angle formed by a horizontal line and a line of sight to a point above ____ 11. for positive numbers a and b, the positive number x such that a x = x b ____ 12. the angle formed by a horizontal line and a line of sight to a point below ____ 13. in a right triangle, the ratio of the length of the leg opposite the angle to the length of the hypotenuse ____ 14. in a right triangle, the ratio of the length of the leg adjacent to the angle to the length of the hypotenuse ____ 15. 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 ____ 16. a ratio of two sides of a right triangle 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 ____ 17. the form of a vector that lists the vertical and horizontal change from the initial point to the terminal point ____ 18. a quantity that has both magnitude and direction ____ 19. two vectors that have the same magnitude and the same direction ____ 20. vectors with the same or opposite direction ____ 21. the vector that represents the sum of two given vectors | → | | → | ____ 22. the length of a vector, written | AB | or | v | | | | | ____ 23. the orientation of a vector, which is determined by the angle the vector makes with a horizontal line 4 ID: A Geometry - Chapter 8 Review 1516 Answer Section SHORT ANSWER 1. ANS: ∆GFJ ∼ ∆GHF ∼ ∆FHJ TOP: 8-1 Similarity in Right Triangles 2. ANS: sin ∠A = 0.45 TOP: 8-3 Solving Right Triangles 3. ANS: m∠P = 53° TOP: 8-3 Solving Right Triangles 4. ANS: 110 feet TOP: 8-1 Similarity in Right Triangles 5. ANS: 26°; 64° TOP: 8-2-Ext. Trigonometric Ratios and Complementary Angles 6. ANS: 5, − 3 TOP: 8-6 Vectors 7. ANS: 402 m TOP: 8-4 Angles of Elevation and Depression COMPLETION 8. ANS: TBD 9. ANS: TBD MATCHING 10. 11. 12. 13. ANS: ANS: ANS: ANS: H I F C TOP: TOP: TOP: TOP: 8-4 Angles of Elevation and Depression 8-1 Similarity in Right Triangles 8-4 Angles of Elevation and Depression 8-2 Trigonometric Ratios 1 ID: A 14. ANS: A 15. ANS: D 16. ANS: E TOP: 8-2 Trigonometric Ratios TOP: 8-2 Trigonometric Ratios TOP: 8-2 Trigonometric Ratios 17. 18. 19. 20. 21. 22. 23. TOP: TOP: TOP: TOP: TOP: TOP: TOP: ANS: ANS: ANS: ANS: ANS: ANS: ANS: H I E A B F D 8-6 Vectors 8-6 Vectors 8-6 Vectors 8-6 Vectors 8-6 Vectors 8-6 Vectors 8-6 Vectors 2