6) Which of the following is closest to the length of the diagonal of a square that has sides that are 60 feet long?
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1 1) The top of an 18-foot ladder touches the side of a building 14 feet above the ground. Approximately how far from the base of the building should the bottom of the ladder be placed? 4.0 feet 8.0 feet 11.3 feet 16.0 feet 2) In a right triangle, if sin then what is tan x? 3) A computer screen has a diagonal dimension of 19 inches and a width of 15 inches. Approximately what is the height of the screen? 4.0 inches 11.7 inches 16.0 inches 24.2 inches 4) Which of the following is the maximum length of pipe, 1 inch in diameter, that will fit inside a rectangular prism 12 inches wide, 16 inches long, and 21 inches tall? 21 inches 26 inches 28 inches 37 inches 5) An escalator in a department store rises 80 feet at a 32 angle, as shown below. What is the distance, x, from the bottom of the escalator to the top of the escalator, to the nearest foot? 94 feet 113 feet 128 feet 151 feet 6) Which of the following is closest to the length of the diagonal of a square that has sides that are 60 feet long? 10.9 feet 84.9 feet 90.0 feet feet
2 7) An airplane is headed for the airport, 15 miles away. If the airplane is at an altitude of 5000 feet, what is the angle of depression, to the nearest tenth of a degree, from the airplane to the airport? (1 mile = 5280 feet) 0.3º 1.0º 3.6º 18.7º 8) Which window with the following dimensions is too small to allow a 48-inch piece of glass to fit through it? 9) Pentagon MNPQR is shown below. What is the length of 10) If the base of a ladder is 5 feet from a building, how long must the ladder be to reach a window in the building that is 15 feet above the ground? 10.0 feet 14.1 feet 15.8 feet 20.0 feet
3 11) The figure below shows If is an isosceles triangle, what is the approximate length of 12) In a right triangle, if what is 13) In a right triangle, which of the following is the definition of the cosine ratio? 14) A radio tower has a support cable attached to its top. The support cable is 140 feet long and it is anchored in the ground 98 feet from the base of the radio tower. How tall is the tower? Give your answer to the nearest foot. 42 feet 100 feet 119 feet 170 feet
4 15) In a right triangle, if tan, then what is sin x? 16) The length of the sides of a triangle are 5, 12, and 13 inches. Which statement is true about this triangle? The area of this triangle is 60 It is an acute triangle It is a right triangle The perimeter of this triangle is 25 in. 17) The entrance to the tent forms an isosceles right triangle as shown, and the support pole, modeled by forms an altitude to the hypotenuse. If how tall is the pole, in feet? ) Three roads intersect to form a large triangular area as shown below. What is the length, to the nearest tenth of a mile, of side x of the triangle? 2.5 miles 2.9 miles 4.0 miles 4.3 miles 19) In a triangle, the length of the hypotenuse is 12 inches. What is the length, in inches, of the side opposite the 60 angle? 6 24
5 20) Andrea wants to prove that in a right triangle, the hypotenuse is twice as long as the shorter leg. She will use below as an example. What should be the concluding statement in Andrea s proof? is a right angle and are complementary 21) The diagram shows the path Kyle walked yesterday. He started at his house, walked to the park, then to the library, and then back home. What is the approximate distance that Kyle walked? 1.25 miles 1.75 miles 2.00 miles 2.15 miles
6 22) A surveyor s notes and drawings are shown below. The drawing shows measurements from A, the top of the mountain, to B, an intermediate site, and from C, a lower peak, to D, the bottom of the mountain. What is the vertical elevation, in feet, from point D to point A on the mountain? ) In a right triangle, if then what is sin x?
7 24) The isosceles right triangle below has an area of 98 square feet. What is the length of the hypotenuse in feet? ) An equilateral triangle has a side length of 12 centimeters. What is the measure, in centimeters, of its altitude? 26) In a right triangle, which of the following is the definition of the tangent ratio? 27) In a right triangle, if, what is?
8 28) In a right triangle, if then what is tan x? 29) Josh tied a helium-filled balloon to a stake in the ground. The wind blew it so that the 10-foot string attached to the balloon made an angle of 45 with the ground. What is the approximate height of the balloon from the ground? 3.2 feet 5.0 feet 7.1 feet 10.0 feet 30) Robert leaves his home to go to his office. He drives 6 km due north and then 4 km due east. Approximately what is the shortest distance from Robert s home to his office, in kilometers?
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