Pythagorean Theorem - Word Problems (Grade 10)

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Pythagorean Theorem - Word Problems

1. 
Sally is sitting 3.5 ft directly behind Jacob. Jacob is sitting 4 ft to the right of Andrew. How far away is Andrew from Sally? Round the answer to the nearest tenth of a foot.
  1. 1.9 ft
  2. 5.3 ft
  3. 7.5 ft
  4. 28.3 ft
2. 
A slide at a playground forms a right triangle. The vertical ladder is 2.5 m tall and the slide is 4 m long. How far away is the end of the slide from the bottom of the ladder? Round the answer to two decimal places.
  1. 3.12 m
  2. 3.20 m
  3. 4.30 m
  4. 4.72 m
3. 
Sarah has a ladder that is 7 meters long. She wants to paint a window frame on the outside of a building. The bottom of the window frame is 4.5 meters above the ground. If she wants the top of the ladder to exactly reach the base of the window frame, how far away from the house should the base of the ladder be? Round the answer to the nearest tenth of a meter.
  1. 3.4 m
  2. 5.4 m
  3. 6.7 m
  4. 8.3 m
4. 
The Great Pyramid of Giza is a square pyramid. The length of one of its base edges is about 230.3 m and its slant height is about 180.3 m. The slant height is the length along one its triangular faces from the center of the base edge to the apex. Using this information, what is the approximate height of the Great Pyramid of Giza, rounded to one decimal place?
  1. 138.7 m
  2. 180.0 m
  3. 213.9 m
  4. 292.5 m
5. 
Jane is flying a plane from Urbenville to Central City, which is located directly northeast of Urbenville. However, new weather information indicates that there is a storm ahead on her current flight path. Jane plans to make a detour, flying directly east for 50 miles and then directly north for another 50 miles, returning to her original flight path. How much additional distance does Jane travel with this detour? Round the answer to the nearest mile.
  1. 29 miles
  2. 50 miles
  3. 90 miles
  4. 100 miles
6. 
The size of a computer monitor is usually described by its diagonal measurement, from corner to corner. If a certain monitor is listed as 25 inches, and its sides make a ratio of 16:9 (width to height), what is the width of the computer monitor? Round the answer to one decimal place.
  1. 8.5 in.
  2. 12.3 in.
  3. 20.0 in.
  4. 21.8 in.
7. 
Christian is setting up his campsite. For his shelter, he is tying a rope between two trees, completely taught, and then setting a tarp over the rope. The distance between the two trees is 12.5 ft. The tarp is stretched over the rope, with no wrinkles, and there is 3 ft of rope left uncovered at each end. When the corners of the tarp are staked directly into the ground, both openings of the tarp shelter form an equilateral triangle. If the rope is 5 ft off the ground, what is the surface area of the tarp? Round the answer to one decimal place.
  1. [math]37.5 \ "ft"^2[/math]
  2. [math]40.4 \ "ft"^2[/math]
  3. [math]53.0 \ "ft"^2[/math]
  4. [math]75.1 \ "ft"^2[/math]
8. 
Andrea is painting the back of her barn. The back of the barn looks like a square with an isosceles right triangle on top (the right angle being at the top). If the height from the ground to the bottom of the roof is 8.3 ft, what is the area she will need to paint? Round the answer to one decimal place.
  1. [math]74.8 \ "ft"^2[/math]
  2. [math]86.1 \ "ft"^2[/math]
  3. [math]103.3 \ "ft"^2[/math]
  4. [math]206.7 \ "ft"^2[/math]
9. 
Carol is putting in a new backsplash on the wall of her kitchen just above the countertop. It will consist of ceramic tiles in the shape of right isosceles triangles, where the hypotenuse side of the triangle will be along the top of the counter with the right angle sticking up. The corners of the tiles (the acute angles in the triangles) will be placed right next to each other, forming a zigzag patter. The counter is 11 ft long, and she she needs to use 44 complete tiles. After applying the tiles to the wall, she wants to put grout along the top edges of the tiles (the legs of the triangles). If she knows from previous work that she needs about half a pound of grout for every foot of tiling, about how much grout will she need? Round the answer to one decimal place.
  1. 3.9 lb
  2. 7.8 lb
  3. 15.6 lb
  4. 124.4 lb
10. 
On his way to school each day, Jim has to walk around a rectangular field that is fenced off. He always walks at the same, constant pace. After arriving at the southeast corner of the field, he walks along the southern end, and then up the western edge to the northwest corner. He knows that the east-west edge of the field takes about 25% less time to walk than the north-south edge does. One day, he notices that the fence has been removed, and now he can walk directly from the southeast corner to the northwest corner. If Jim's new path is 30 ft shorter than the old one, what is the length of the diagonal across the field that Jim now walks? Round the answer to one decimal place, if necessary.
  1. 12.5 ft
  2. 15 ft
  3. 75 ft
  4. 113.2 ft

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