Determine if the following triangles are right...
Transcript of Determine if the following triangles are right...
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Lesson 8.1 Unit 8 Homework Key
Determine if the following triangles are right triangles or not using the Pythagorean Theorem.
1. 2. 3.
Yes, right triangle Yes, right triangle No, not right triangle
4. 5. 6.
No, not right triangle Yes, right triangle Yes, right triangle
7. π = 12 ππ‘ 8. π = 12 ππ 9. π = 10 ππ
π = 16 ππ‘ π = 35 ππ π = 24 ππ
π = 25 ππ‘ π = 37 ππ π = 27 ππ
No, not right triangle Yes, right triangle No, not right triangle
10. π = 20 ππ‘ 11. π = 5 ππ 12. π = 5 ππ
π = 21 ππ‘ π = 12 ππ π = 12 ππ
π = 29 ππ‘ π = 17 ππ π = 13 ππ
Yes, right triangle No, not right triangle Yes, right triangle
17 ππ
15 ππ
8 ππ
25 ππ 24 ππ
7 ππ
6 π
7 π
8 π
14 ππ
10 ππ
8 ππ
41 ππ 40 ππ
9 ππ
6 π
8 π
10 π
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Lesson 8.2
Find the length of the missing side of each right triangle. Round your answers to three decimal places if necessary. 1. 2. 3. π β 38.974 ππ π = 21 π π = 5 ππ‘ 4. 5. 6. π β 22.913 ππ π = 48 ππ π β 5.831 ππ 7. 8. 9. π¦ = 17 ππ π§ = 53 ππ‘ π₯ β 26.458 ππ 10. 11. 12. π = 24 ππ β = 5 π π₯ = 11 ππ
π 40 ππ
9 ππ π
29 π 20 π π
3 ππ‘
4 ππ‘
π 25 ππ
10 ππ π
73 ππ 55 ππ
π
3 ππ
5 ππ
15 ππ π¦
8 ππ
π§
45 ππ‘
28 ππ‘
π 26 ππ
10 ππ
40 ππ
π₯
30 ππ
β
13 π 12 π
61 ππ
60 ππ
π₯
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13. 14. 15. π‘ β 18.735 ππ π β 20.616 ππ π₯ = 35 ππ‘ Solve the following problems. Round your answers to the nearest whole number when necessary. 16. Youβre locked out of your house, and the only open window is on the second floor 25 feet above the ground. There are bushes along the side of the house that force you to put the base of the ladder 7 feet away from the base of the house. How long of a ladder will you need to reach the window?
β 26 ππππ‘ 17. Shae takes off from her house and runs 3 miles north and 4 miles west. Tired, she wants to take the shortest route back. How much farther will she have to run if she heads straight back to her house?
5 πππππ 18. Televisions are advertised by the length of their diagonals. If a 42 inch television measures 18 inches high, how wide is the television?
β 38 πππβππ 19. A soccer field is 100 yards by 60 yards. How long is the diagonal of the field?
β 117 π¦ππππ 20. Leonard walks 14 meters south and 48 meters east to get to school. If he takes the straight path home after school, how far will he have to walk?
50 πππ‘πππ 21. You place a 24 foot ladder 10 feet away from the house. The top of the ladder just reaches a window on the second floor. How high off the ground is the window?
β 22 ππππ‘ 22. The dimensions of a basketball court are 74 feet and 42 feet. What is the length of the diagonal of the court?
β 85 ππππ‘
π‘ 20 ππ
7 ππ
π 45 ππ
40 ππ
π₯
21 ππ‘
28 ππ‘
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23. Televisions are advertised by the length of their diagonals. If a TV measures 22 inches high and 45 inches wide, by what size will the TV be advertised.
β 50 ππ 24. A rectangular garden measures 5 feet wide by 12 feet long. If a hose costs $5 per foot, how much would it cost to place a hose through the diagonal of the garden?
$65 25. A football field is 160 feet wide and 360 feet long. The coach wants to put spray paint along the diagonal of the field. If the spray paint costs approximately $1 per foot of coverage, how much should the coach budget for spray paint?
β $394 26. A rectangular park measures 8 miles long by 6 miles wide. The park director wants to put a fence along both sides of the trail that runs diagonally through the park. If the fence costs $150 per mile, how much will it cost to buy the fence?
$3000 27. A rectangular pool has a diagonal of 17 yards and a length of 15 yards. If the paint costs $2 per yard of coverage, how much will it cost the owner to paint the width of both ends of the pool?
$32 28. A rectangular dog pen is 3 meters by 4 meters. If a chain costs $1.75 per meter, how much would it cost to put a chain along the diagonal of the pen?
$8.75 29. Architects built a doorway that was 4 feet wide by 7 feet tall. The diagonal measured 7.3 feet. Are the angles in the doorway right angles?
No 30. A rectangular garden measures 3 meters wide by 4 meters long. The diagonal of the garden measures 5 meters. Are the angles in the garden right angles?
Yes
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Lesson 8.3
Use the picture below to find information about the pyramid with a square base in problems 1-14. Round your answers to three decimal places if necessary.
1. The pyramid has a square base that is 70 ππ‘ on each side. The slant height is 37 ππ‘. What is β, the height of the pyramid?
12 ππ‘
2. The pyramid has a square base that is 120 ππ on each side. The slant height is 61 ππ. What is β, the height of the pyramid?
11 ππ
3. The pyramid has a square base that is 50 π on each side. The slant height is 30 π. What is β, the height of the pyramid?
β 16.583 π
4. The pyramid has a square base that is 14 ππ on each side. The slant height is 25 ππ. What is β, the height? 24 ππ
5. The pyramid has a square base that is 14 ππ on each side. The height is 24 ππ. What is π, the slant height?
25 ππ 6. The pyramid has a square base that is 24 ππ‘ on each side. The height is 5 ππ‘. What is π, the slant height?
13 ππ‘ 7. The pyramid has a square base that is 70 ππ on each side. The height is 10 ππ. What is π, the slant height?
β 36.401 ππ 8. The pyramid has a square base that is 26 ππ‘ on each side. The height is 82 ππ‘. What is π, the slant height?
β 83.024 ππ‘ 9. The height of the pyramid is 15 ππ, and the slant height is 39 ππ. Find the value of π in the diagram.
36 ππ 10. The height of the pyramid is 80 ππ, and the slant height is 82 ππ. Find the value of π in the diagram.
18 ππ 11. The slant height is 17 ππ‘ and the height is 8 ππ‘. What is π , the side length of the base?
30 ππ‘ 12. The slant height is 10 ππ and the height is 8 ππ. What is π , the side length of the base?
12 ππ 13. The slant height is 26 ππ and the height is 10 ππ. What is π , the side length of the base?
48 ππ 14. The slant height is 50 ππ‘ and the height is 32 ππ‘. What is π , the side length of the base?
β 76.837 ππ‘
β
slant height
π
π
6
π
β
slant height
π
Use the picture below to find information about the pyramid in problems 15-26. Round your answers to three decimal places if necessary.
15. The cone has a radius of 12 ππ and a height of 5 ππ. What is π, the slant height of the cone?
13 ππ
16. The cone has a radius of 15 ππ and a height of 8 ππ. What is π, the slant height of the cone?
17 ππ
17. The cone has a radius of 24 ππ and a height of 70 ππ. What is π, the slant height of the cone?
74 ππ
18. The cone has a radius of 40 ππ and a height of 42 ππ. What is π, the slant height of the cone? 58 ππ
19. The cone has a radius of 30 ππ‘ and a slant height of 34 ππ‘. What is β, the height of the cone?
16 ππ‘
20. The cone has a radius of 33 π and a slant height of 65 π. What is β, the height of the cone? 56 π
21. The cone has a radius of 16 ππ and a slant height of 20 ππ. What is β, the height of the cone?
12 ππ 22. The cone has a radius of 30 ππ and a slant height of 50 ππ. What is β, the height of the cone?
40 ππ 23. The cone has a height of 16 ππ and a slant height of 65 ππ. What is π, the radius of the cone?
63 ππ 24. The cone has a height of 48 ππ‘ and a slant height of 50 ππ‘. What is π, the radius of the cone?
14 ππ‘ 25. The cone has a height of 4 ππ and a slant height of 6 ππ. What is π, the radius of the cone?
β 4.472 ππ 26. The cone has a height of 14 ππ and a slant height of 55 ππ. What is π, the radius of the cone?
β 53.188 ππ
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Use the picture below to find lengths of segments in the rectangular prism in problems 27-38. Round your answers to three decimal places if necessary.
27. The length of π΄π΅Μ Μ Μ Μ is 6 ππ‘ and the length of π΅πΆΜ Μ Μ Μ is 8 ππ‘. Find the length of π΄πΆΜ Μ Μ Μ . 10 ππ‘
28. The length of π΄π΅Μ Μ Μ Μ is 40 ππ and the length of π΅πΆΜ Μ Μ Μ is 42 ππ. Find the length of π΄πΆΜ Μ Μ Μ . 58 ππ
29. The length of π΄π΅Μ Μ Μ Μ is 23 ππ and the length of π΅πΆΜ Μ Μ Μ is 70 ππ. Find the length of π΄πΆΜ Μ Μ Μ . β 73.682 ππ
30. The length of π΄π΅Μ Μ Μ Μ is 7 ππ and the length of π΅πΆΜ Μ Μ Μ is 7 ππ. Find the length of π΄πΆΜ Μ Μ Μ . β 9.899 ππ
31. The length of π΄πΆΜ Μ Μ Μ is 13 ππ and the length of π·πΆΜ Μ Μ Μ is 84 ππ. Find the length of π΄π·Μ Μ Μ Μ . 85 ππ
32. The length of π΄πΆΜ Μ Μ Μ is 5 ππ‘ and the length of π·πΆΜ Μ Μ Μ is 12 ππ‘. Find the length of π΄π·Μ Μ Μ Μ . 13 ππ‘
33. The length of π΄πΆΜ Μ Μ Μ is 11 ππ and the length of π·πΆΜ Μ Μ Μ is 30 ππ. Find the length of π΄π·Μ Μ Μ Μ . β 31.953 ππ
34. The length of π΄πΆΜ Μ Μ Μ is 5 ππ and the length of π·πΆΜ Μ Μ Μ is 4 ππ. Find the length of π΄π·Μ Μ Μ Μ .
β 6. 403 ππ
35. The length of π΄π΅Μ Μ Μ Μ is 4 ππ‘, the length of π΅πΆΜ Μ Μ Μ is 3 ππ‘ and the length of π·πΆΜ Μ Μ Μ is 12 ππ‘. Find the length of π΄π·Μ Μ Μ Μ . 13 ππ‘
36. The length of π΄π΅Μ Μ Μ Μ is 12 ππ, the length of π΅πΆΜ Μ Μ Μ is 5 ππ and the length of π·πΆΜ Μ Μ Μ is 84 ππ. Find the length of π΄π·Μ Μ Μ Μ . 85 ππ
37. The length of π΄π΅Μ Μ Μ Μ is 2 ππ‘, the length of π΅πΆΜ Μ Μ Μ is 3 ππ‘ and the length of π·πΆΜ Μ Μ Μ is 10 ππ‘. Find the length of π΄π·Μ Μ Μ Μ . β 10.630 ππ‘
38. The length of π΄π΅Μ Μ Μ Μ is 6 ππ the length of π΅πΆΜ Μ Μ Μ is 8 ππ and the length of π·πΆΜ Μ Μ Μ is 50 ππ. Find the length of π΄π·Μ Μ Μ Μ . β 50.990 ππ
A B
C
D
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Lesson 8.4
Determine the distance between the given points. Round your answers to three decimal places if necessary.
1. (1, 3) and (4, 7) 5 π’πππ‘π 2. (β3, 3) and (2, β9) 13 π’πππ‘π
2.
3. (β2, β5) and (3, β8) β 5.831 π’πππ‘π 4. (β3, β3) and (3, 3) β 8.485 π’πππ‘π
5. (3, β2) and (5, 0) β 2.828 π’πππ‘π 6. (β3, β9) and (β3, 9) 18 π’πππ‘π
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7. (2, 1) and (3, β3) β 4.123 π’πππ‘π 8. (4, β2) and (7, 2) 5 π’πππ‘π
9. (1, 1) and (7, 9) 10 π’πππ‘π 10. (β8, 2) and (6, 2) 14 π’πππ‘π
11. (β4, 6) and (6, 2) β 10.770 π’πππ‘π 12. (2, 4) and (5, β2) β 6.708 π’πππ‘π
13. (β5, β3) and (6, 6) β 14.213 π’πππ‘π 14. (β5, 4) and (7, 3) β 12.042 π’πππ‘π
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15. (β9, β3) and (β4, 4) β 8.602 π’πππ‘π 16. (2, β4) and (5, 4) β 8.544 π’πππ‘π
17. (0, 7) and (4, 2) β 6.403 π’πππ‘π 18. (β8, 7) and (7, β5) β 19.209 π’πππ‘π
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Lesson 8.5
Answer the following questions either using π β π. ππ or giving your answer in terms of π . Round your answer to the nearest hundredth where necessary.
1. Find the volume of a cylinder with a radius of 3 ππ and a height of 10 ππ. 90π ππ3 β 282.6 ππ3
2. Find the volume of a cylinder with a radius of 10 ππ and a height of 2 ππ.
200π ππ3 β 628 ππ3
3. Find the volume of a cylinder with a radius of 5 ππ and a height of 15 ππ. 375π ππ3 β 1177.5 ππ3
4. Find the volume of a cylinder with a diameter of 22 π and a height of 5 π.
605π π3 β 1899.7 π3
5. Find the volume of a cylinder with a diameter of 4 ππ‘ and a height of 1 ππ‘. 4π ππ‘3 β 12.56 ππ‘3
6. Find the volume of a cylinder with a radius of 9 ππ and a height of 9 ππ.
729π ππ3 β 2289.06 ππ3
7. Find the volume of a can of green beans with a radius of 3 ππ and a height of 8 ππ. 72π ππ3 β 226.08 ππ3
8. Find the volume of a cylindrical can of oatmeal with a radius of 8 ππ and a height of 45 ππ.
2880π ππ3 β 9043.2 ππ3
9. Find the volume of a cylindrical water bottle with a diameter of 4 ππ and a height of 30 ππ. 120π ππ3 β 376.8 ππ3
10. Find the volume of a can of Pepsi with a diameter of 2 ππ and a height of 3.5 ππ.
3.5π ππ3 β 10.99 ππ3
11. Find the volume of a water pipe with a radius of 0.75 ππ‘ and a length of 16 ππ‘. 9π ππ‘3 β 28.26 ππ‘3
12. Find the volume of a straw used for drinking with a radius of 2 ππ and a height of 170 ππ.
680π ππ3 β 2135.2 ππ3
β
π
12
13. Find the volume of a cone with a radius of 3 ππ and a height of 10 ππ. 30π ππ3 β 94.2 ππ3
14. Find the volume of a cone with a radius of 10 ππ and a height of 3 ππ. 100π ππ3 β 314 ππ3
15. Find the volume of a cone with a radius of 5 ππ and a height of 15 ππ. 125π ππ3 β 392.5 ππ3
16. Find the volume of a cone with a radius of 12 π and a height of 5 π. 240π π3 β 753.6 π3
17. Find the volume of a cone with a diameter of 4 ππ‘ and a height of 9 ππ‘. 12π ππ‘3 β 37.68 ππ‘3
18. Find the volume of a cone with a diameter of 18 ππ and a height of 9 ππ. 243π ππ3 β 763.02 ππ3
19. Find the volume of a waffle cone for ice cream with a radius of 4 ππ and a height of 12 ππ. 64π ππ3 β 200.96 ππ3
20. Find the volume of a cone birthday hat with a radius of 2 ππ and a height of 9 ππ. 12π ππ3 β 37.68 ππ3
21. Find the volume of a funnel with a diameter of 10 ππ and a height of 9 ππ. 75π ππ3 β 235.5 ππ3
22. Find the volume of a sphere with a diameter of 6 ππ. 36π ππ3 β 113.04 ππ3
23. Find the volume of a sphere with a diameter of 18 ππ. 972π ππ3 β 3052.08 ππ3
24. Find the volume of a sphere with a radius of 6 ππ. 288π ππ3 β 904.32 ππ3
25. Find the volume of a sphere with a radius of 12 π. 2304π π3 β 7234.56 π3
26. Find the volume of a sphere with a radius of 2 ππ‘. 10.67π ππ‘3 β 33.49 ππ‘3
27. Find the volume of a sphere with a radius of 5 ππ. 166.67π ππ3 β 523.33 ππ3
28. Find the volume of a mini basketball with a radius of 3.5 ππ. 57.17π ππ3 β 179.51 ππ3
29. Find the volume of the Earth with a diameter of approximately 12, 756 ππ. 3.46 Γ 1011π ππ3 β 1.09 Γ 1012 ππ3
30. Find the volume of the moon with a diameter of approximately 3475 ππ. 6.99 Γ 109π ππ3 β 2.20 Γ 1010 ππ3
31. Find the volume of a gumball with a radius of 3 ππ. 36π ππ3 β 113.04 ππ3
π
β
π
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Lesson 8.6
Answer the following questions using π β π. ππ. Round your answer to the nearest hundredth where necessary. 1. Find the height of a cylinder with a volume of 30 ππ3 and a radius of 1 ππ.
β β 9.55 ππ 2. Find the height of a cylinder with a volume of 100 ππ3 and a radius of 2 ππ.
β β 7.96 ππ 3. Find the height of a cylinder with a volume of 720π ππ‘3 and a radius of 6 ππ‘.
β = 20 ππ‘ 4. Find the height of a cylinder with a volume of 1215π ππ3 and a radius of 9 ππ.
β = 15 ππ 5. Find the radius of a cylinder with a volume of 950 ππ3 and a height of 10 ππ.
π β 5.5 ππ 6. Find the radius of a cylinder with a volume of 208 ππ3 and a height of 4 ππ.
π β 4.07 ππ 7. Find the radius of a cylinder with a volume of 108π ππ‘3 and a height of 12 ππ‘.
π = 3 ππ‘ 8. Find the radius of a cylinder with a volume 686 ππ3 and a height of 14 ππ.
π β 3.95 ππ 9. Find the height of a cone with a volume of 150 ππ3 and a radius of 10 ππ.
β β 1.43 ππ 10. Find the height of a cone with a volume of 21 ππ‘3 and a radius of 4 ππ‘.
β β 1.25 ππ‘ 11. Find the radius of a cone with a volume of 175 ππ3 and a height of 21 ππ.
π β 2.82 ππ 12. Find the radius of a cone with a volume of 196π ππ3 and a height of 12 ππ.
π = 7 ππ 13. Find the radius of a sphere with volume β 113.04 ππ3.
π = 3 ππ 14. Find the radius of a sphere with volume β 904.32 ππ3.
π = 6 ππ 15. Find the radius of a sphere with volume β 3052.08 π3.
π = 9 π 16. Find the radius of a sphere with volume β 4.186Μ ππ‘3.
π = 1 ππ‘
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Lesson 8.7
Answer the following questions using π β π. ππ and rounding your answer to the nearest hundredth where necessary.
1. Find the volume of a cone used for the tip of a rocket with a diameter of 12 π¦ππ and a height of 15 π¦ππ .
180π π¦ππππ 3 β 565.2 π¦ππππ 3
2. Find the volume of a pencil with a radius of 0.5 ππ, a cone height of 3 ππ, and a cylinder height of 14 ππ.
3.75π ππ3 β 11.78 ππ3
3. Find the volume of a model rocket with a radius of 1 ππ, a cone height of 3 ππ, and a cylinder height of 8 ππ.
ππ πππ β ππ. ππ πππ
4. Find the volume of a caulking gun with a radius of 2 ππ, a cone height of 3 ππ, and a cylinder height of 20 ππ.
84π ππ3 β 263.76 ππ3
5. Find the volume of a crayon with a radius of 2 ππ, a cone height of 21 ππ, and a cylinder height of 80 ππ.
348π ππ3 β 1092.72 ππ3
6. Find the volume of a model jet with a radius of 1 ππ‘, a cone height of 3 ππ‘, and a cylinder height of 6 ππ‘.
7π ππ‘3 β 21.98 ππ‘3
7. Find the radius of a pencil with a volume of 110π ππ3, a cone height of 3 ππ, and a cylinder height of 10 ππ.
π β 3.16 ππ
8. Find the radius of a model rocket with a volume of 2500 ππ3, a cone height of 6 ππ, and a cylinder height of 25 ππ.
π β 5.43 ππ
9. Find the cylinder height of a caulking gun with a volume of 300 ππ3, a cone height of 6 ππ, and a radius of 2 ππ.
h β 21.89 ππ
10. Find the cone height of a pencil with a volume of 750 ππ3, a radius of 3 ππ, and a cylinder height of 25 ππ.
h β 4.62 ππ
Visual for questions
1-10
15
Visual for questions
13-14
π
11. Find the volume of a propane gas tank with half spheres on either end
that has a radius of 3 ππ‘ and a length (π) of 7 ππ‘.
99π ππ‘3 β 310.86 ππ‘3
12. Find the volume of a submarine with half spheres on either end that has a radius of 6 π and a length (π) of 15 π.
828π π3 β 2599.92 π3
13. Find the volume of a grain silo with a half sphere on one end that has a diameter of 6 π and a height (β) of 15 π.
153π π3 β 480.42 π3
14. Find the volume of a grain silo with a half sphere on one end that has a diameter of 6 ππ‘ and a height (β) of 35 ππ‘.
333π ππ‘3 β 1045.62ππ‘3
Visual for questions
11-12
π