applied mathematics - unit 3: geometry in engineering, architecture, and fine arts part 2

roy is creating a miniature model of the kitchen in his parents' restaurant using a ratio of 1 : 5. there are two refrigerators in the kitchen that are 1.5 m tall and 2 m wide. both have a depth of 1 m. how much space will the refrigerators occupy in roy's model?

0.048 m^3

a pyramid art installation has a surface area of 24 m^2. an artist creates replicas with scale factors of 1/8, 1/10, and 1/12. what is the surface area of each replica? match each scale factor with its correct surface area.

0.33 of 1 scale factor of 1/8 : 3.00 m^3 scale factor of 1/10 : 2.40 m^3 scale factor of 1/12 : 0.17 m^3

the approximate volume of the statue of liberty is 2500 m^3. a gift shop sells a replica with a scale factor of 1/18. what is the approximate volume of the replica?

0.43 m^3

kiara is drawing a photo of a car using a scale factor of 3. the radius for each of the car's tires is 2 cm. what will the area of a tire in kiara's drawing be?

113 cm^2

the length, width, and height of a wooden crate are 1 m, 3 m, and 2 m. what is the maximum number of such crates that can be transported in a cargo ship with a storage hold that has a volume of 72,000 m^3?

12,000

the angle of elevation of a ladder is 19∘ and the ladder is 12 feet from the wall. what is the height of the ladder in feet?

12.7 ft

jacob designs a building with a square base. he starts by building a model for the building, which has a base with an area of 36 feet. the base of the real building will have an area of 6084 ft. what is the scale factor between the model and the real building?

13

the length of one leg of a right triangle is 6 units. what is the approximate length of the second leg if the hypotenuse is 3 times the length of the given leg?

17 units

the army corps of engineers has been instructed to measure the effectiveness of a special wireless satellite tower's signal at various distances. the height of the satellite tower is 250 feet. if the tower's signal reaches its equipment truck, which forms an angle of elevation of 55∘, approximately how far is the truck from the base of the tower?

175 feet

a statue that is 80 m tall stands on 625 m^2 base. an artist creates a replica using a ratio of 1 : 15. what is the area of the replica's base?

2.78 m^2

the angle of depression from a descending airplane to the control tower below is 60∘. if the plane is 35,000 feet above the ground, approximately what is the plane's horizontal distance from the control tower?

20,207 ft

a snail farmer's business is growing. he wants to build a new pen similar to the old one, but with a scale factor of 1:3. this will accommodate the expanding business. the old pen is square. if the diagonal of the old pen measures 10 meters, what is the length of one side of the new pen? use the pythagorean theorem.

21.21 m

a park ranger at the top of a 700-meter station sees a fair that is 1800 m from the base of the tower. what is the angle of elevation?

21.3 degrees

mike has a plaster replica of the eiffel tower in his room. the volume of the plaster in the replica is 0.25 m^3. he wishes to make a bigger replica using a scale factor of 5. what is the volume of plaster that he needs for the new replica?

31.25 m^3

if the hypotenuse is a side of the pyramid, and the pyramid has a height of 28 m, what is the angle of depression from the apex of the pyramid to the ground below?

50.5

an architect designs a castle tower for a new attraction at a popular amusement park. blueprints of the tower, which is in the shape of a rectangular prism, show that it is 47 cm tall, 23 cm in length, and 25 cm in width. the blueprints have a scale factor of 1 : 96. calculate the actual surface area of the tower.

5218.1 m^2

a building that is 150 m tall, 100 m wide, and 80 m deep has glass on all sides except the roof and the base. what is the area of the glass needed for this building?

54,000 m^2

kevin rode his bike 2 miles east and 6 miles north from his home to the movie theater, forming a right angle. how far is the movie theater from kevin's home?

6.32 miles

an architectural firm wants to replicate a nearby estate with some changes. the new estate will be larger than the original by a scale factor of 1:10. a section of the roof in the original estate is constructed using 45-45-90 triangles. the hypotenuse of the triangle is 10 meters long. what will be the length of the triangle legs for the larger estate?

70.71 m

andrea made a replica of the empire state building. the surface area of the model is 45 feet. what is the surface area of the actual empire state building in ft. if the scale factor is 44?

87120 ft^2

tommy is constructing a roof for a tree house. he decides to use 45∘ 45∘ 90∘ triangles with legs that are 8 feet in length to create the roof's frame. if the hypotenuse is the width of the house, which answers represent its length? select all that apply.

8√2 ft. 11.31 ft. √8^2 + 8^2 ft

kamal made a replica of the kaaba located in mecca, saudi arabia. the dimensions of his replica are 24 cm long bu 21 cm wide by 30 cm high. what is the surface area of the actual kaaba in meters if the scale factor is 50?

927 m^2

examine this short piece of music for the guitar: which notes would best continue the pattern?

fc

lesson 15

periodic functions in music and art

what are the basic characteristics of music that display periodic behavior?

pitch and rhythm

lesson 13

pythagorean theorem and special right triangles

consider triangle def. the measure of angle f is 90∘, de = 85 cm, ef = 84 cm, and df = 13 cm. which of the following expressions are true about this triangle? select all that apply.

sin e = 13/85 tan d = 84/13 cos e = 84/85

what are the correct trigonometric ratios for angle h in a right triangle if gi = 5, hi = 12, and gh = 13?

sin h = 5/13, cos h = 12/12, tan h = 5/12

catalina extends a ladder 15 feet and places it diagonally on a tree to get her cat that is perched on the lowest branch. which trigonometric ratio would she use to determine how high her cat was from the ground if the ladder formed a 65∘ angle with the ground?

sine

lesson 11

surface area in architecture and art

a computer science engineer is developing a model of a motherboard to use in product demonstrations. the original motherboard measures 5 1/4 inches in length. the model needs to be scaled up at a factor of 8 : 1. what would the length of the model be?

the model would be 42 inches long.

an artist is asked to scale up a model of pluto to 3 times its original size. if the original model of pluto has a radius of 12 cm, what is the volume of the new model?

the volume of the new model of pluto is 195,432.20 cm^3.

students measure the sides of 4 triangles in a test. the lengths of the sides of the different triangles follow: using the pythagorean theorem, which of the triangles are right triangles? select all that apply.

triangle 2, triangle 3

lesson 14

trigonometric ratios in engineering, science, and architecture

lesson 12

volume in engineering, architecture, and art

does the image display periodic behavior? why or why not? select the answer that is completely true.

yes, because the pattern of curving lines repeats to form spirals that flow into each other.