Similar and Congruent Triangles- Word Problems (Grade 10)

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Similar and Congruent Triangles- Word Problems

1. 
Sam is standing near a tree. If Sam is 6 feet tall and casts an 11 foot shadow, and the tree casts a 30 foot shadow, how tall is the tree? Round the answer to 1 decimal place, if necessary.
  1. 2.2 ft
  2. 16.4 ft
  3. 55 ft
  4. Not enough information.
2. 
Kayla and Josh are flying kites. They have both let out all the string for their kites, which is 25 m. The angle of elevation of Kayla's kite is 40°. The angle of elevation of Josh's kite is 50°. If Kayla's kite is currently 16.1 m above the ground, how high is Josh's kite?
  1. 8.9 m
  2. 16.1 m
  3. 19.1 m
  4. It cannot be determined with the information given.
3. 
Anne is trying to determine the width of a river that flows from east to west. She is currently standing on the south side of the river, very near the river's edge. Directly across the river, almost touching the water, is a large tree. She knows that she can create two similar triangles to measure the width of the river. She begins walking due west for 21 ft, and then walks 10 ft south. Looking directly at the large tree she noticed earlier across the river, she walks towards the river in a north-easterly direction. When she arrives at the river, she sees that she is exactly 14 ft west of her original starting point. How wide is the river at the point from which she was originally standing? Round the answer to one decimal place if necessary.
  1. 20 ft
  2. 15 ft
  3. 9.8 ft
  4. 6.7 ft
4. 
A large ladder is leaning against a wall. The base of the ladder is 10 ft away from the wall and it forms a 51.3° angle with the ground. A smaller ladder is also leaning against the wall. It's base is also 10 ft away from the wall, but it forms a 38.7° angle with the ground. If the smaller ladder reaches 8 ft up the wall, how high does the larger ladder reach up the wall? Round the answer to one decimal place, if necessary.
  1. 4.5 ft
  2. 8 ft
  3. 12.5 ft
  4. Not enough information.
5. 
Andrew is trying to determine the height of a building. He has a small mirror and places it flat on the ground, face up, 4.4 m away from the base of the building. He then backs away from the mirror, until he can see the top of the building in it; he is 50 cm away from the mirror when this happens. If Andrew is 1.85 m, and his eyes are 5 cm below the top of his head, how high is the building? Round the answer to 1 decimal place.

Note: In flat mirrors, the angle of incidence (the angle between the incoming light ray and a line perpendicular to the mirror at the point the light ray strikes) is equal to the angle of reflection (the angle between the light ray leaving the mirror and the perpendicular line referenced already).
  1. 0.2 m
  2. 15.8 m
  3. 16.3 m
  4. 21.0 m
6. 
Colin is scuba diving and trying to locate a ship wreck. The ship wreck is at the bottom of the ocean, about 40 meters below the water's surface. When Colin initially jumped into the water from the boat he traveled in, he was directly above the sunken ship. However, as he dove down, the current pushed him away from the ship wreck. He is now 20 meters below the surface of the water, but cannot see the ship wreck at the bottom of the ocean because it is too dark. However, he can see the bottom of the boat from which he dove into the ocean, which hasn't moved. If his line of sight to the bottom of the boat makes a 35° angle above a horizontal line from him parallel to the bottom of the ocean, at what angle below this horizontal line will he need to dive at to reach the sunken ship?
  1. 90°
  2. 55°
  3. 35°
  4. Not enough information.
7. 
A pinhole camera is a simple camera that has a lightproof box with one tiny hole. As light enters the small hole, an inverted image of what's in front the camera appears on the opposite side of the box. Savanna has set up a pinhole camera on a flat stand, and it captures the image of a tree which is standing almost perfectly upright. If the image inside the pinhole camera's box is 1 foot tall, the width of the box is 1.5 feet, and the distance from the tree to the front side of the pinhole camera is 14 feet, how tall is the tree? Round the answer to one decimal place, if necessary.
  1. 5.7 ft
  2. 9.3 ft
  3. 18.7 ft
  4. 21 ft
8. 
Mark and Sharon are standing side by side. Then, Mark begins walking N45°E at a speed of 1.6 m/s. Sharon starts walking at the same time, at a speed of 1.3 m/s, in the direction S60°E. If they are about 106.8 m apart after one minute, about how far apart are they after another minute of walking at the same speed and in the same direction?
  1. 184.8 m
  2. 202.8 m
  3. 213.6 m
  4. 280.8 m
9. 
Sam is checking on an experiment that is being conducted in an open field. There are three almost identical small plants, which have been planted in different places in the field. Starting at a large boulder, the first plant is 8.3 ft directly east. The second plant is 14.1 ft directly south of the first plant. The third plant is 9.7 ft directly east of the second plant. Sam has to follow these directions each time he comes, in order to find the plants. However, after checking the third plant, he walks directly back to the boulder from where he started. When Sam is walking back to the boulder after checking all the plants and he crosses his earlier path where he walked between the first and second plants, about how far south of the first plant is he? Round the answer to one decimal place.
  1. 6.5 ft
  2. 7.6 ft
  3. 12.3 ft
  4. 16.5 ft
10. 
Marcus is standing 15 ft away from the edge of a cliff, which overlooks the ocean and is 40 ft tall. The cliff is completely vertical, forming a right angle with the land at the top and the water at the bottom. If Marcus is 6.1 ft tall, and a boat sailing away from land just emerges into view beyond the cliff edge, how far is the line of sight distance to the boat? Round the answer to one decimal place.
  1. 56.3 ft
  2. 106.2 ft
  3. 113.4 ft
  4. 122.4 ft

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