1. A maintenance technician sights the top of a telephone pole at a 25 angle of elevation as shown.

Transcription

1 Name 1. A maintenance technician sights the top of a telephone pole at a 25 angle of elevation as shown. Determine the horizontal distance between the technician and the base of the telephone pole to the nearest tenth of a foot. 2. In the three right triangles shown, m C = m F = m I = 36 Complete the statements about the triangles by dragging the correct choices into the proper locations. Not all the choices will be used. Drag and drop the choices into the appropriate boxes. Because each triangle contains a right angle and a 36 angle, the triangles are and AB = DE =. The proportion shows that the ratio of the length of the leg AC DF opposite the 36 angle to the length of the will be the same for any right triangle with a 36 angle. The value of the ratio is defined to be the of 36. 1

2 3. A square has sides that are each 90 feet long. Which equations can be used to calculate d, the length of a diagonal of the square, in feet? Select ALL that apply. A. d = 1 (90 90) 2 B. d = C. d = D. cos 45 = 90 d E. sin 45 = 90 d F. tan 45 = 90 d 4. A carpenter is constructing a triangular roof for a storage shed as shown in the figure. Part A How high will the peak of the roof rise above the top of the shed? Give your answer to the nearest foot. Enter your answer in the box feet After the roof is constructed, it will be covered with an asphalt roofing material. The carpenter needs to calculate the combined length of the two sloping sides. What will be the total length needed by the roof covering? Give your answer to the nearest foot. Enter your answer in the box feet 2

3 5. Part A Alex is visiting a local shopping mall that has a rectangular shape with a diagonal walkway that goes from the entrance of the mall to the food court. The floor plan is shown. Alex needs to stop at the sports store on the way to the food court. How much longer, in feet does he walk than if he walks directly from the entrance to the food court along the diagonal walkway? Show work to justify your answer. A walkway connects the restroom and the sports store. The restroom and electronics store are both at the midpoints of their respective walkways. A separate walkway, which is perpendicular to the walkway between the entrance and the sports store, connects the restroom to the electronics store. What is the distance, in feet, of the walkway that connects the restroom to the electronics store? Show work to justify your answer. Enter your answer and work in the space provided. 3

4 6. City workers will be hanging cable between two poles. The poles are 20 feet apart and perpendicular to the ground. The cable will cross back and forth between equally spaced anchors placed on the poles and will be pulled tight. A section of the design is show in the figure. Let n represent the total number of anchors placed on the two poles. Create an expression to represent the length, in feet, a cable needed for n anchors. Explains how you determine the values in your expression. Enter your expression and your explaination in the space provided. 4

5 7. The figure shows right ABC Which of the listed are equal to the sine of B? Select all that apply. A. b c B. c a C. b a D. the cosine of B E. the cosine of C F. the cosine of (90 B) G. the sine of (90 C) 5

6 8. Part A A merry-go-round is set up at a local fair. The merry-go-round moves continuously at a rate slow enough for riders to step on and off the ride. The pink horse, P, moves along the circumference of the ride. Hal used a coordinate grid to make a rough sketch of the merry-go-round, with the center at the origin. Initially, P is at P(5,0). It takes 30 seconds for P to return to the same place. What is the rate at the merry-go-around is turning, in feet per minute? Show your work. Enter your answer and your work in the space provided. What would be the coordinate of P on Hal s sketch after 8.25 minutes? Enter your answers in the boxes. 6

7 9. In circle O, points A, B, C, and D lie on the circle. AD is congruent to BC, and the measure of AB is twice the measure of BC. Part A Select from the drop- down menus to correctly complete the statement. The measure of ACD is the measure of ADC. Select from the drop-down menus to correctly complete the statement. The measure of ADC is the measure of BCD. 10. Circle T is shown. Lines PS and line RS are tangent to circle T. Part A What is the measure, in degrees, of PTR? What is the measure, in the degrees of PQR? 7

8 11. The circle has a radius of 12 units. Shade an area 24π square units. Divide the circle into the correct number of sections. Then, select the number of sections to represent the answer. 12. Part A A circle in the xy- coordinate plane has the equation x 2 + y 2 + 6y 4 = 0. If the equation of the circle is written in the form x 2 + (y + k) 2 = c, where k and c constants, what is the value of k? What is the radius of the circle? A. 2 B. 4 C. 13 D The equation x 2 10x + 17 = y 2 2y describes a circle in the coordinate plane. Find the radius of the circle and the coordinates of its center. Enter your answers in the spaces provided. Enter only your answers. Radius = units center: (, ) 8

9 14. The figure illustrates an informal argument for the formula for the area of a circle. The circle is divided into congruent sectors, and the sectors are rearranged to form a shape that resembles a parallelogram, as shown. As the number of sectors increases, the rearranged shape more closely resembles a parallelogram with area A, given by the formula = bh, where b is the base and h is the height of a parallelogram. Select the correct value for b and h to develop the area of a circle in terms of r, the radius of the circle. 15. The figure shows a circle with center P and inscribed isosceles ABC. If AC has the same length as the radius of the circle, what is the measurement ABC? Degrees. 9

10 16. The above-ground swimming pool in Lien s backyard is shaped like a right circular cylinder with a diameter 12 feet and height 4 feet. The pool is filled with water to a height of 3.5 feet. One person who is completely in the water will displace about 18 gallons of water. (Note: 1 cubic foot is approximately 7.48 gallons.) Lien is inviting high school classmates to swim in the pool. Create a model to determine the greatest number of classmates who can be in the pool before the water overflows. Explain your reasoning. Enter your model and your explanation in the space provided. 17. Part A The number of people who live in a unit of area is called population density of the area. It is usually given as people per square mile or per square kilometer. A map of the Orchard Hill Neighborhood Is shown. The population of the Orchard Hill Neighborhood is 360 people. The length of each block is the same and the length of 20 blocks is 1 mile. What is the area in square miles of Orchard Hill? A square mile B square miles C square miles D square miles What is the population density of the Orchard Hill Neighborhood, given as a number of people per square mile? 10

11 18. A queen- sized mattress is 20 inches longer than it is wide. A king- sized mattress is 16 inches wider than the queen-sized mattress but has the same length. The area of the king-sized mattress is 1,280 square inches more than that of the queen-sized mattress. Part A Write an equation that can be used to determine the area of the king-sized mattress. Define all variables provided. Determine the dimensions of the king- sized and queen- sized mattresses. Show your work. Enter your answer and your work in the space provided. 11

12 19. Hank is putting jelly candles into two containers. One container is a cylindrical jar with a height of 33.3 centimeters and a diameter of 8 centimeters. The other container is spherical. Hank determines that the candles are cylindrical in shape and that each candy has a height of 2 centimeters and a diameter of 1.5 centimeters. He also determines that air will take up 20% of the volume of the containers. The rest of the space will be taken up by the candles. Part A After Hank fills the cylinder jar with candies, what will be the volume, in cubic centimeters, of the air in the cylinder jar? Round your answer to the nearest whole cubic centimeter. Enter your answer in the box. What is the maximum number of the candles that will fit in the cylindrical jar? Part C The spherical container can hold a maximum of 260 candies. Approximate the length of the radius, in centimeters, of the spherical container. Round your answer to the neatest tenth. Part D Hank is filling the cylindrical container using bags of candy that have a volume of 150 cubic centimeters. Air takes up 10% of the volume of each bag, and the rest of the volume is taken up by candy. How many bags of candy are needed to fill the cylindrical container with 260 candies? 12

13 20. A landscaper designed a display of flowers for an area in a public park. The flower seeds will be planted at points that lie on a circle that has diameter of 8 feet. The point where any seed is planted must be at least 2 feet away from the seeds on either side of it. Part A What is the maximum number of flower seeds that can be planted using the design? After planting the flower seeds, the landscaper has 20 seeds left over. The landscaper wants to plant all of the remaining seeds in another circle so that the seeds are 2 feet apart. To the nearest tenth of a foot, what is the diameter of the smallest circle that the landscaper can use to plant all of the remaining seeds? Enter your answer in the box 13

14 21. Each of the two-dimensional figures shown will be rotated 360 about the respective line, creating a three- dimensional figure. Put the number of the appropriate two-dimensional figure to identify the correct representation of the resulting three-dimensional figure

15 22. The given cylindrical container is used to fill the rectangular prism fish tank with water. What is the least number of full cylindrical containers needed to completely fill the fish tank? 15