~ 1 ~ Geometry 2 nd Semester Review Find the value for the variable for each of the following situations
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1 Geometry nd Semester Review 018 Find the value for the variable for each of the following situations m y. 8.9 cm slide 4.1 meters long makes an angle of 5 with the ground. To the nearest tenth of a meter, how far above the ground is the top of the slide? ~ 1 ~
2 1. The students in Mr. ollin s class used a surveyor s measuring device to find the angle from their location to the top of a building. They also measured their distance from the bottom of the building. To the nearest foot, find the height of the building. uilding 100 ft 18. n airplane over the Pacific sights an atoll at an angle of depression of 5. t this time, the horizontal distance from the airplane to the atoll is 469 meters. What is the height of the plane to the nearest meter? 19. To find the height of a pole, a surveyor moves 140 feet away from the base of the pole and then, with a transit 4 feet tall, measures the angle of elevation to the top of the pole to be 44. To the nearest foot, what is the height of the pole? 14. The Sears Tower in hicago is 1450 feet high. model of the tower is 4 inches tall. What is the ratio of the height of the model to the height of the actual Sears Tower? 0. Find the angle of elevation of the sun from the ground to the top of a tree when a tree that is 10 yards tall casts a shadow 14 yards long. Round to the nearest degree. 15. Find the length of the leg. If your answer is not an integer, leave it in simplest radical form Find the area of the following figures. 1. Equilateral triangle with sides of 10 cm.. ircle with diameter of 1 in. Find the area of the sector. 16. Find the length of the hypotenuse Viola drives 170 meters up a hill that 0 makes an angle of 6 with the horizon. To the nearest tenth of a meter, what horizontal distance has she covered? 4. Identify the quadrilateral. Find the measure of the angles. 1 ~ ~
3 5. Draw an Isosceles Trapezoid with base angles of ( + 5) o and ( 5) 0. Find. 1. Find the measure of the missing eterior angle of a pentagon given that four of the eterior angles are Find the measure of each interior angle of the given regular polygon. 6. Heagon. Sum of all the angles? 7. Dodecagon Each angle measures:. If the sides of a pentagon are in a ratio of 4 to 7, what would the ratio of their perimeters be?. Find the similarity ratio between two cubes whose volumes are 79 m and 75 m. 4. Find the length of arc XPY. Leave answers in terms of pi. X 8. Solve the given proportion. 4 m Y P 5. Find the length of arc. Leave answer in terms of pi. 9. Find the length of the altitude drawn to the hypotenuse. Leave answer in square root form Draw a net for the given figure. 0. D ~ WXYZ. If D 6, D and WZ 59, find YZ. ~ ~
4 Find the value of the variable for each of the following diagrams O 5 8. D 4. 5 P Find when = 0, = 6 and D = 8. 1 D Find the measure of <O when m<r = 8. N O Q ~ 4 ~ R
5 46. Find the measure of <. 51. O 5 mm Find the measure of < when arc DE = 10 and arc = mm D mm mm E Find the surface area and the volume for each of the following figures. 5. Write the equation of the given circle in standard form. y m 19 m 14 cm 5 m O cm 54. What is the radius and the center of the following circle: 50. ( 6) ( y 5) m 10 m ~ 5 ~
6 Factor the following completely a 15 h 10h 4 m 11mn 18n If m F 5 10 and m F 0, find. 60. DEFG is a rectangle. DF = - and EG = 1. Find the value of and the length of each diagonal. 66. lassify the triangle. 61. Find the midpoint of (-4, 7) and (5, -1). 67. In trapezoid DEFG, find m D. 6. Find the distance between (5,6) and (-, 8). 6. Find the value for the variable. 68. Describe the relationship between the diagonals of a rhombus. (two things) a. b. 69. Name all of the quadrilaterals whose diagonals are perpendicular. 64. Find the value of and y. ~ 6 ~
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