Honors Geometry Chapter 8 Test Review Name Find the geometric mean between each pair of numbers. 1. 9 and 14 2. 20 and 80 3. 8 2 3 and 4 2 3 4. Find x, y and z. 5. Mike is hanging a string of lights on his barn for a square dance. Using a book to sight the top and bottom of the barn, he can see he is 15 feet from the barn. If his eye level is 5 feet from the ground, how tall is the barn? 6. A room-in-attic truss is a truss design that provides support while leaving area that can be enclosed as living space. In the diagram, BCA and EGB are right angles, BEF is isosceles, CD is an altitude of ABC, and EG is an altitude of BEF. If DB = 5 feet, CD = 6 feet 4 in., BF = 10 feet 10 in. and EG = 4 feet 6 in. what is AE? Round to the nearest tenth.
7. Refer to the figure at the right. The orthocenter of ABC is located 6.4 units from point D. Find BC. Round to the nearest tenth. 8. The geometric mean of a number and four times the number is 22. What is the number? Determine whether each set of numbers can be the measures of the sides of a triangle. If so, classify the triangle as acute, obtuse or right. 9. 7, 24, 25 10. 13, 15, 16 11. 65, 72, 88 12. Alexi walks 27 meters south and 38 meters east to get around a lake. Her sister swims directly across the lake. How many meters to the nearest tenth did Alexi s sister save by swimming? 13. Find the perimeter.
14. If the perimeter of square 2 is 200 units and the perimeter of square 1 is 150 units, what is the perimeter of square 3? 15a. Find x. 15b. 16. The screen aspect ratio, or the ratio of the width to the length, of a high-definition television is 16:9. The size of a television is given by the diagonal distance across the screen. If an HDTV is 41 inches wide, what is its screen size? Use special right triangles to find x and y. 17. 18. 19. 20.
21. Jason is adding a climbing wall to his little brother s swing set. If he starts building 5 feet out from the existing structure, and wants it to have a 60⁰ angle, how long should the climbing wall be? 22. The top of the aquarium coffee table shown is an isosceles right triangle. The table s longest side, AC, measures 107 centimeters. What is the distance from vertex B to side AC? What are the lengths of the other two sides? 23. Determine the length of the leg of a 45-45-90 triangle with a hypotenuse length of 11. 24. Find the length of the hypotenuse of a 45-45-90 triangle with a leg of 8 centimeters. 25. An equilateral triangle has an altitude length of 18 feet. Determine the length of a side of the triangle. Use trigonometry to find x. Round to the nearest tenth. 26. 27. 28.
Use trigonometry and a calculator to find the measure of R to the nearest degree. 29. 30. 31. 32. Find the tangent of the greater acute angle in a triangle with side lengths of 3, 4 and 5 centimeters. 33. Find the cosine of the smaller acute angle in a triangle with side lengths of 10, 24, and 26 inches. 34. Ethan and Tim want to estimate the area of the field that their team will use for soccer practice. They know that the field is rectangular, and they have paced off the width of the field as shown. They used the fence posts at the corners of the field to estimate that the angle between the length of the field and the diagonal is about 40⁰. If they assume that each of the steps is about 18 inches, what is the area of the practice field to the nearest square foot? 35. Find x and y. 36. Sarah s cat climbed up a tree. If she sights her cat at an angle of elevation of 40⁰ and her eyes are 5 feet off the ground, how high up from the ground is her cat?
37. Two buildings are sited from atop a 200 meter skyscraper. Building A is sited at a 35⁰ angle of depression, while Building B is sighted at a 36⁰ angle of depression. How far apart are the two buildings to the nearest meter? 38. There is a cell phone tower in the field across from Jen s house. If Jen walks 50 feet from the tower, and finds the angle of elevation from her position to the top of the tower to be 60⁰, how tall is the tower? 39. Tom delivers papers on a rural route from his car. If he throws a paper from a height of 4 feet, and it lands 15 feet from the car, at what angle of depression did he throw the paper to the nearest degree? Use Law of Sines or Law of Cosines to find x. Round angle to the nearest degree and side measures to the tenth. 40. 41. 42. 43.