Name: 
 

Pre Algebra Chapter 11


Multiple Choice
Identify the choice that best completes the statement or answers the question.
 
 
Simplify the square root.
 

 1. 
mc001-1.jpg
a.
16
b.
0.4
c.
40
d.
4
 

 2. 
–mc002-1.jpg
a.
–0.5
b.
5
c.
–5
d.
–25
 
 
Estimate the square root to the nearest integer.
 

 3. 
mc003-1.jpg
a.
6
b.
5
c.
7
d.
4
 

 4. 
–mc004-1.jpg
a.
–4
b.
–5
c.
–2
d.
–3
 

 5. 
Find two integers that make the equation mc005-1.jpg true.
a.
5, –5
b.
5, 0.5
c.
mc005-2.jpg
d.
5, 25
 

 6. 
Which of these sets of numbers contains no irrational numbers?
a.
mc006-1.jpg, mc006-2.jpg, –8.15
c.
mc006-4.jpg, mc006-5.jpg
b.
mc006-3.jpg
d.
mc006-6.jpg
 

 7. 
Which of these sets of numbers contains no rational numbers?
a.
mc007-1.jpg
c.
–6, mc007-3.jpg, 4mc007-4.jpg
b.
mc007-2.jpg, –13
d.
mc007-5.jpg
 

 8. 
The surface area of the top surface of the water in a circular swimming pool is about 206 square feet. Estimate the radius of the pool, to the nearest foot.
a.
about 14 feet
b.
about 8 feet
c.
about 11 feet
d.
about 10 feet
 

 9. 
Which number is rational?
a.
mc009-1.jpg
b.
mc009-2.jpg
c.
mc009-3.jpg
d.
mc009-4.jpg
 

 10. 
Which number is irrational?
a.
mc010-1.jpg
b.
mc010-2.jpg
c.
mc010-3.jpg
d.
mc010-4.jpg
 
 
In the given right triangle, find the missing length.
 

 11. 
mc011-1.jpg
a.
28 m
b.
26 m
c.
25 m
d.
27 m
 

 12. 
mc012-1.jpg
a.
10 m
b.
14 m
c.
21 m
d.
28 m
 
 
In the given right triangle, find the missing length to the nearest tenth.
 

 13. 
mc013-1.jpg
a.
20.2 ft
b.
7.5 ft
c.
11.7 ft
d.
17.3 ft
 

 14. 
mc014-1.jpg
a.
3.7 ft
b.
15.7 ft
c.
5.9 ft
d.
12.1 ft
 

 15. 
Two flag poles in front of the Court House are 12 ft tall. The distance from the top of one pole to the base of the other as shown in the diagram is 20 ft. What is the distance between the two flag poles?
mc015-1.jpg
a.
16 ft
b.
23 ft
c.
18 ft
d.
15 ft
 
 
The lengths of two sides of a right triangle are given. Find the length of the third side. Round to the nearest tenth if necessary.
 

 16. 
legs: 28 in. and 15 in.
a.
37.5 in.
b.
23.6 in.
c.
29.6 in.
d.
31.8 in.
 

 17. 
leg: 20 m; hypotenuse: 25 m
a.
10.5 m
b.
8.9 m
c.
32 m
d.
15 m
 

 18. 
Which of the following could NOT be the lengths of the sides of a right triangle?
a.
9 ft, 12 ft, 15 ft
c.
4 cm, 7.5 cm, 8.5 cm
b.
5 in., 10 in., 15 in.
d.
1.5 m, 2 m, 2.5 m
 
 
Find the distance between the two points. Round to the nearest tenth if necessary.
 

 19. 
(8, 8), (12, 11)
a.
7
b.
5
c.
25
d.
28
 

 20. 
(–2, –6), (3, 9)
a.
15.8
b.
250
c.
3.2
d.
20
 

 21. 
(2, 5) and (–1, –5)
a.
1
b.
109
c.
10.4
d.
3
 

 22. 
(–2, –1) and (3, 5)
a.
4.1
b.
2.2
c.
3.6
d.
7.8
 

 23. 
Find the perimeter of WXYZ. Round to the nearest tenth if necessary.
mc023-1.jpg
a.
3.2
b.
23.4
c.
152
d.
21.3
 

 24. 
Find the perimeter of mc024-1.jpg. Round to the nearest tenth.
mc024-2.jpg
a.
90.0
b.
18.0
c.
14.3
d.
10.5
 
 
Find the midpoint of the segment with the given endpoints.
 

 25. 
D(1, 2) and E(–3, 6)
a.
(–7, 10)
b.
(–2, 2)
c.
(–1, 4)
d.
(4, 64)
 

 26. 
A(3, –5) and C(2, 9)
a.
(–1, 5.5)
b.
(0.5, –7)
c.
(2.5, 2)
d.
(8, –7)
 

 27. 
M(–2, 1) and O(–3, 2)
a.
(–2.5, 1.5)
b.
(–0.5, –0.5)
c.
(0.5, –0.5)
d.
(–3, –5)
 

 28. 
Find the midpoint of mc028-1.jpg.
mc028-2.jpg
a.
(3, 1)
b.
(1, 1)
c.
(10, 4)
d.
(4, 4)
 

 29. 
Find the midpoints of the sides of the quadrilateral shown below.
mc029-1.jpg
a.
(–1, 1), (–4, –1), (–1, –3), (2, –1)
c.
(1, –1), (–1, –4), (–3, –1), (–1, 2)
b.
(1, –1), (4, 1), (1, 3), (–2, 1)
d.
(–1, 1), (1, 4), (3, 1), (1, –2)
 

 30. 
M(–3, –1) is the midpoint of mc030-1.jpg. If S has coordinates (4, 6), what are the coordinates of R?
a.
(–10, –8)
b.
(–10, 13)
c.
(11, 13)
d.
(11, –8)
 
 
Write a proportion and find the value of x in the diagram. Round to the nearest tenth if necessary.
 

 31. 
mc031-1.jpg
mc031-2.jpg
Not drawn to scale
a.
mc031-3.jpg; 10
c.
mc031-5.jpg; 5
b.
mc031-4.jpg; 18.3
d.
mc031-6.jpg; 18.3
 

 32. 
mc032-1.jpg
mc032-2.jpg
a.
mc032-3.jpg; 8.9
c.
mc032-5.jpg; 13.7
b.
mc032-4.jpg; 13.7
d.
mc032-6.jpg; 8.9
 

 33. 
Charlene made the sketch below in order to find the height x of a pole. She positioned a mirror on the ground so that she could see the reflection of the top of the pole. Her height, her distance from the mirror, and her line of sight to the mirror determine the smaller triangle. The pole’s height, its distance from the mirror, and the distance from the top of the pole to the mirror form a larger similar triangle. Find the height of the pole to the nearest tenth.
mc033-1.jpg
a.
16.5 ft
b.
22.0 ft
c.
20.5 ft
d.
17.5 ft
 

 34. 
Find the length of the hypotenuse. Round to the nearest tenth if necessary.
mc034-1.jpg
a.
6.9 ft
b.
2.8 ft
c.
5.7 ft
d.
8 ft
 

 35. 
The legs of an isosceles right triangle are 11 cm long. Find the length of the hypotenuse. Round to the nearest tenth if necessary.
a.
15.6 cm
b.
22 cm
c.
7.8 cm
d.
19.1 cm
 

 36. 
Ingrid is making a quilt using squares that measure 5 in. on a side. What is the length of a diagonal of one of the quilt squares? Round to the nearest tenth.
a.
8.7 in.
b.
7.1 in.
c.
3.5 in.
d.
14.2 in.
 

 37. 
In mc037-1.jpg, mc037-2.jpg is a right angle and mc037-3.jpg = 45. If AB = 19 feet, what is BC?
a.
32.9 ft
b.
16.5 ft
c.
26.9 ft
d.
19.0 ft
 
 
Find the missing lengths in the triangle. Round to the nearest tenth if necessary.
 

 38. 
mc038-1.jpg
a.
x = 8 in., y = 2.8 in.
c.
x = 8 in., y = 6.9 in.
b.
x = 6.9 in., y = 8 in.
d.
x = 12 in., y = 6.9 in.
 

 39. 
mc039-1.jpg
a.
a = 7.5 cm, b = 10.6 cm
c.
a = 7.5 cm, b = 13 cm
b.
a = 13 cm, b = 7.5 cm
d.
a = 5 cm, b = 13 cm
 

 40. 
mc040-1.jpg
a.
c = 6 in., d = 3 in.
c.
c = 9 in., d = 10.4 in.
b.
c = 3 in., d = 6 in.
d.
c = 9 in., d = 27 in.
 

 41. 
In a 30mc041-1.jpg-60mc041-2.jpg-90mc041-3.jpg triangle, the length of the side opposite the 30mc041-4.jpg angle is 9 mm. Find the length of the side opposite the 60mc041-5.jpg angle and the length of the hypotenuse.
a.
mc041-6.jpg mm, mc041-7.jpg mm
c.
mc041-8.jpg mm, mc041-9.jpgmm
b.
9 mm, 18 mm
d.
mc041-10.jpg mm, 18 mm
 

 42. 
The length of the hypotenuse of a 30mc042-1.jpg-60mc042-2.jpg-90mc042-3.jpg triangle is 28 m. Find the length of the side opposite the 30mc042-4.jpg angle.
a.
7 m
b.
14 m
c.
mc042-5.jpg m
d.
mc042-6.jpg m
 

 43. 
Which of the following CANNOT be the lengths of a 30mc043-1.jpg-60mc043-2.jpg-90mc043-3.jpg triangle?
a.
5, 10, mc043-4.jpg
b.
12, 6, mc043-5.jpg
c.
4, 2, mc043-6.jpg
d.
mc043-7.jpg, mc043-8.jpg, mc043-9.jpgmc043-10.jpg
 

 44. 
For mc044-1.jpg, find the sine, cosine, and tangent of mc044-2.jpg.
mc044-3.jpg
a.
sin P = mc044-4.jpg, cos P = mc044-5.jpg, tan P = mc044-6.jpg
c.
sin P = mc044-10.jpg, cos P = mc044-11.jpg, tan P = mc044-12.jpg
b.
sin P = mc044-7.jpg, cos P = mc044-8.jpg, tan P = mc044-9.jpg
d.
sin P = mc044-13.jpg, cos P = mc044-14.jpg, tan P = mc044-15.jpg
 

 45. 
Use the diagram to find tan A as a fraction in simplest form.
mc045-1.jpg
a.
mc045-2.jpg
b.
mc045-3.jpg
c.
mc045-4.jpg
d.
mc045-5.jpg
 

 46. 
Use the diagram to find cos B as a fraction in simplest form.
mc046-1.jpg
a.
mc046-2.jpg
b.
mc046-3.jpg
c.
mc046-4.jpg
d.
mc046-5.jpg
 

 47. 
Use the diagram to find sin X as a fraction in simplest form.
mc047-1.jpg
a.
mc047-2.jpg
b.
mc047-3.jpg
c.
mc047-4.jpg
d.
mc047-5.jpg
 
 
Use a calculator to find the given value. Round to four decimal places.
 

 48. 
tan 27mc048-1.jpg
a.
0.8910
b.
1.9626
c.
0.4540
d.
0.5095
 

 49. 
sin 21mc049-1.jpg
a.
0.3584
b.
2.7904
c.
0.9336
d.
0.3839
 

 50. 
cos 21mc050-1.jpg
a.
1.0711
b.
0.9336
c.
0.3839
d.
0.3584
 

 51. 
Find the value of a in the diagram of the right triangle. Round to the nearest tenth.
mc051-1.jpg
a.
21.6 in.
b.
24.2 in.
c.
5.0 in.
d.
12.3 in.
 

 52. 
Find the value of x in the diagram of the right triangle. Round to the nearest tenth.
mc052-1.jpg
a.
21.7
b.
15.1
c.
14.6
d.
29.2
 

 53. 
A slide 4.8 m long makes an angle of 28mc053-1.jpg with the ground. How high above the ground is the top of the slide?
a.
2.3 m
b.
4.2 m
c.
2.6 m
d.
1.5 m
 

 54. 
Wires are attached to a pole to make it more secure. The diagram shows one of those wires having a length of 220 feet. The angle of elevation from the ground to the top of the pole is 36mc054-1.jpg. What is the height of the pole?
mc054-2.jpg
a.
178.0 ft
b.
374.3 ft
c.
159.8 ft
d.
129.3 ft
 

 55. 
A ladder leans against a building forming an angle of 55mc055-1.jpg with the ground as shown in the diagram. The base of the ladder is 5 feet from the building. What is the length of the ladder?
mc055-2.jpg
a.
9.1 feet
b.
6.1 feet
c.
7.1 feet
d.
8.7 feet
 

 56. 
A large totem pole near Kalama, Washington, is 106 feet tall. At a particular time of day, the angle of elevation to the top of the pole from the end of the shadow it casts is 23mc056-1.jpg. What is the length of the shadow? Round to the nearest tenth.
mc056-2.jpg
a.
115.2 ft
b.
45.0 ft
c.
271.3 ft
d.
249.7 ft
 

 57. 
The figure below shows a flashlight beam shining on the heads of three people such that it hits exactly at the top of each head. The angle of elevation from the ground to the top of each of the three heads is 45mc057-1.jpg. Person A is 4 feet tall, Person B is 5.5 feet tall, and Person C is 6.5 feet tall. How far away from the flashlight is each person?
mc057-2.jpg
a.
4 feet, 5 feet, 6 feet
c.
4 feet, 5.5 feet, 6.5 feet
b.
4.5 feet, 5.5 feet, 6.5 feet
d.
6.9 feet, 9.5 feet, 11.3 feet
 

 58. 
Maria looks at the top of a building at an angle of elevation of 63mc058-1.jpg. She is standing 50 feet from the base of the building and her eyes are 5.5 feet from the ground. How tall is the building, to the nearest tenth of a foot?
mc058-2.jpg
a.
103.6 feet
b.
50.1 feet
c.
98.1 feet
d.
28.2 feet
 

 59. 
A ranger spots a forest fire while standing on a 26-meter observation tower. The angle of depression from the tower to the fire is 23mc059-1.jpg. To the nearest meter, how far is the fire from the base of the tower?
a.
28 m
b.
61 m
c.
67 m
d.
11 m
 

 60. 
Jennie is working at a lighthouse. From the top of the lighthouse, she spots a boat at an angle of depression of 25mc060-1.jpg. She knows that the landmark rock located next to the boat is 600 feet from the bottom of the lighthouse. What is Jennie’s elevation? Round to the nearest foot.
a.
1,287 feet
b.
280 feet
c.
254 feet
d.
544 feet
 

 61. 
Jared is standing on the roof of a 100-meter building doing some surveying. He spots a delivery truck at an angle of depression of 30mc061-1.jpg. How far is the truck from the base of the building? Round to the nearest meter.
a.
200 meters
b.
5,774 meters
c.
173 meters
d.
115 meters
 

 62. 
Max is in a control tower at a small airport. He is located 50 feet above the ground when he spots a small plane at an angle of depression of 27mc062-1.jpg. What is the distance of the plane from the base of the tower? Round to the nearest foot.
a.
25 feet
b.
110 feet
c.
56 feet
d.
98 feet
 

Short Answer
 
 
Identify the number as rational or irrational. Explain.
 

 63. 
291.87
 

 64. 
sa064-1.jpg
 

 65. 
Is a triangle with sides of length 3 m, 4 m, and 5 m a right triangle? Explain.
 

 66. 
Is a triangle with sides of length 6 ft, 21 ft, 23 ft a right triangle? Explain.
 

 67. 
A new park is placed on a coordinate plane to help in locating important features of the park. The diagram below shows the vertices of the quadrilateral defined by the fences of the park.
sa067-1.jpg
a.At the midpoint of each side, the Park Commission will have an entrance gate. Find the midpoints of the sides. Call the midpoint of sa067-2.jpg M, the midpoint of sa067-3.jpg O, the midpoint of sa067-4.jpg X, and the midpoint of sa067-5.jpg Y.
b.Find the perimeter of the quadrilaterals PARK and MOXY. If necessary, round to the nearest tenth.
c.Compare the perimeters of PARK and MOXY.
 

 68. 
A building lot in a city is shaped as a 30sa068-1.jpg-60sa068-2.jpg-90sa068-3.jpg triangle. The side opposite the 30sa068-4.jpg angle measures 41 feet.
a.Find the length of the side of the lot opposite the 60sa068-5.jpg angle.
b.Find the length of the hypotenuse of the triangular lot.
c.Find the sine, cosine, and tangent of the 30sa068-6.jpg angle in the lot. Write your answers as decimals rounded to four decimal places.
 

 69. 
Zack is building a model sailboat. The mast will have two inches of height below the base of the main sail, as shown in the diagram below. He wants the base of the sail to have a length of 11 inches and sa069-1.jpg to measure 49sa069-2.jpg.
sa069-3.jpg
a.Write an equation that can be used to find the length of the side of the triangular sail opposite sa069-4.jpg.
b.Find the length of the side of the triangle opposite sa069-5.jpg, to the nearest tenth.
c.What will be the height of the mast, to the nearest tenth?
 

 70. 
Charlie is at a small airfield watching for the approach of a small plane with engine trouble. He sees the plane at an angle of elevation of 32sa070-1.jpg. At the same time, the pilot radios Charlie and reports the plane’s altitude is 1,700 feet. Charlie’s eyes are 5.2 feet from the ground.
a.Draw a sketch of this situation.
b.Find the ground distance from Charlie to the plane. Explain your work.
 

Essay
 

 71. 
Skip bought a lot on which he wants to build a house. The lot is a square with an area of 10,000 square feet.
a.Let s be the length of the side of the lot. Write an equation that models this situation. Explain the equation.
b.Find the length of one side of the lot.
c.Skip plans to build a house with a length of 39 feet and a width of 43 feet. What percent of the lot will be covered by the house? Round to the nearest whole percent. Explain your method for solving this problem.
 

 72. 
Vance built a triangular sand box for his daughter. The measures of the lengths of the sides are 21 feet, 28 feet, and 37 feet.
a.Explain how you know the sand box is not in the shape of a right triangle.
b.What should the lengths of the sides be in order for the sand box to form one right angle? Explain your reasoning.
 

 73. 
Orlando is surveying at a mine. He made the diagram below to help him find the distance x across a mining pit.
es073-1.jpg
a.Assume that es073-2.jpg. Write a proportion that includes the length x. Explain the proportion.
b.Find the length x. Explain your method for finding this length.
c.Find the length of es073-3.jpg. Explain your method.
d.Find the length of es073-4.jpg. Explain your method.
e.What is the length of es073-5.jpg?
 

 74. 
A swimming pool is a square with a side length of 92 feet. A portion of the pool is roped off for a triangular kiddie pool as shown in the diagram below.
es074-1.jpg
a.Find the length of the side of the kiddie pool opposite the es074-2.jpg angle. Explain your method for finding the length.
b.Find the perimeter of the triangular kiddie pool. Explain your method for finding the perimeter.
c.Find the perimeter of the other portion of the pool. Explain your method for finding the perimeter.
 

 75. 
A pilot flying at 3,900 feet spots a dock on a lake at an angle of depression of es075-1.jpg. In the diagram below, the pilot is located at point A, the dock is located at point C, and the angle of depression is es075-2.jpg.
es075-3.jpg
a.DC is the distance on the ground from the plane to the dock. Use a trigonometric ratio to find DC to the nearest foot. Show your work.
b.Find the measure of the angle of elevation es075-4.jpg. Explain your method for finding the angle.
c.Use a trigonometric ratio to find AC to the nearest foot. Show your work.
 

Other
 

 76. 
The City Commission wants to construct a new street that connects Main Street and North Boulevard, as shown in the diagram below.
ot076-1.jpg
Not drawn to scale

a.What will be the length of the new street? Explain how you found this length.
b.The construction cost has been estimated at $140 per linear foot. Estimate the cost for constructing the street. Explain your method for finding the estimate.
 

 77. 
On Echo’s Farm, individual fields are laid out in rectangles like WBSA on the coordinate plane below. The units marked are in feet.
ot077-1.jpg

a.What is the area of the field WBSA? Explain your method for finding the area.
b.In order to avoid stepping on crops, you walk from the shed (S) to the well (W) by first walking to point A. Using this route, how far is it from the shed to the well? Explain your method for finding the distance.
c.What is the shortest distance between the shed and the well? Explain your method for finding this distance.
 

 78. 
Jose is planting a square garden. He measures the diagonal of the garden and finds that it measures about 6.5 meters in length. Find the approximate length of a side of the garden. Explain your method for finding the length.
 

 79. 
The diagram below shows a 30ot079-1.jpg-60ot079-2.jpg-90ot079-3.jpg triangle.
ot079-4.jpg
a.Find the lengths of the missing sides. Show how to find the lengths.
b.Find the sine,cosine, and tangent of 30ot079-5.jpg. Write as decimals rounded to four decimal places.
c.Find the sine, cosine, and tangent of 60ot079-6.jpg. Write as decimals rounded to four decimal places.
d.Describe any relationships between the trigonometric ratios for 30ot079-7.jpg and the trigonometric ratios for 60ot079-8.jpg.
 



 
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