Name: Date: Period: Geometry Review- Chapter 10 1. The diagonal of a rectangle measures 15 cm long, and the width is 10. Find the height of the rectangle and epress your answer in simplest radical form. y 2. Find e, and epress your answer in simplest radical form. (9, 12) e 0 3. a) Roberto installs roof tiles for a living, and has put his ladder up against a customer s house. When he first gets to the house, he puts the bottom of the ladder 10 feet from the base of the house, and it reaches 24 feet up the wall of the house. How long is the ladder? Draw a diagram please!
3. b) Roberto moves to a different house, and places the ladder 2 feet closer to the house than his first customer. How far up the house does the ladder reach on the new customer? Round your answer to the nearest thousandth foot. Draw a new diagram! 3. c) Roberto goes to a new house where the roof is 14 feet high. Is it logical for him to use the same ladder? Eplain. 35 4. Find the value of. 13 37 5. Find the values of and y. 15 y 45 o
6. Find the values of the indicated variables. If you answer is not an integer, please epress your answer in simplest radical form. w = 5 in = y = 45 o w z = y 30 o z 7. Mrs. Day is flying her propeller plane at an altitude of 2,000 feet. She see s the banana plant she s going to in Africa at an angle of depression of 35 o. What is the approimate length of her horizontal distance from the cornfield. Round your answer to the nearest whole number, and make sure you draw and label a picture! 8. According to the General Requirements for Curb Ramps, the maimum running slope of a ramp leading up to a curb is 1:8. That means for a ramp being built, for every 8 inches in length it can only rise 1 inch. For a ramp with the maimum allowable height of 3 inches, what is the angle that the ramp makes with the ground? Record your answer to the nearest thousandth degree.
9. A utility pole broke and fell as shown. What was the original height of the pole? Justify your answer in a complete sentence. 11 ft. 60 ft. 10. Cynthia has 3 metal pipes, one 10 feet long, one 11 feet long, and one 12 feet long. If she connected them end to end, would they form a right triangle? Justify your answer. 11. Triangle ABC has side lengths of 4, 5, and 8. Is ABC an acute, right, and obtuse triangle? Justify your answer in a complete sentence. 12. Find the value of. Epress your answer in simplest radical form. 14 45 o
13. Find the value of. Epress your answer in simplest radical form. 14 60 o 14. Find LO. Epress your answer in simplest radical form. O L 30 o 6 M 15. What is the perimeter of a square with an 18-inch long diagonal? Epress your answer in simplest radical form. 16. Find the value of. Round your answer to the nearest thousandth inch. 49 o 19
17. Write out FOUR equations you could use to find the value of. Use Sin, Cos, Tan, and Pythagorean theorem to write your equations. 14 62.3 o 27.7 o 16 18. Eplain, using complete sentences, why sin(30) = cos (60). 2 60 o 30 o 3 19. Romero wants to know the height of a building. He measures a distance of 45 feet from the base of the building and stands at that spot. He then measures a 67 o angle of elevation to the top of the building. His eyes are at a height of 4 feet above the grount. How tall is the building? Round to the nearest thousandth of a foot. Include a labeled diagram with your work! 20. Find the value of. Round your answer to the nearest thousandth degree. 7 ft 15 ft. o 26 o