Use the provided image along with the Pythagorean theorem to find the distance between locations around town. Look for right Triangles! Use the answer choices at the bottom to drag and drop the correct Distance between each of the buildings. All answers have been rounded to the nearest 10th.
Image: [A right triangle is shown with a building at the right angle, and two other buildings at the ends of the other two sides. The distances between the buildings are labeled as follows:
Building A to Building B = 40 meters
Building A to Building C = 30 meters
Building B to Building C = 50 meters
]
Answer choices:
a) 10 meters
b) 50 meters
c) 60 meters
To find the distance between Building A and Building B, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Let's denote the distance between Building A and Building B as x. Then, we have:
x^2 = 30^2 + 40^2
x^2 = 900 + 1600
x^2 = 2500
x = √2500
x = 50 meters
Therefore, the distance between Building A and Building B is 50 meters.
Let's now find the distance between Building B and Building C. Using the Pythagorean theorem again, we have:
x^2 = 40^2 + 50^2
x^2 = 1600 + 2500
x^2 = 4100
x = √4100
x = 64.1 meters
Therefore, the distance between Building B and Building C is 64.1 meters.
Using the answers choices provided:
- Distance between Building A and Building B = 50 meters
- Distance between Building A and Building C = 30 meters
- Distance between Building B and Building C = 64.1 meters
Drag and drop the answers to the correct pairs:
a) 10 meters - None
b) 50 meters - Distance between Building A and Building B
c) 60 meters - Distance between Building B and Building C