Question

The distance from building 1 to building 2 is 2,000 feet. The distance between building 2 and building 3 is 5,000 feet. The distance between building 1 and 3 is 1,000 feet. Do the building form a right triangle? Why or why not

Answer 1

To determine if the buildings form a right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
Let's label the buildings as A, B, and C, where A is building 1, B is building 2, and C is building 3. Then, we can determine the lengths of the three sides of the triangle as follows:
AB = 2000 feet BC = 5000 feet AC = 1000 feet
Now, we can check whether the Pythagorean theorem holds true:
(AB)^2 + (BC)^2 = (2000)^2 + (5000)^2 = 29,000,000
(AC)^2 = (1000)^2 = 1,000,000
Since (AB)^2 + (BC)^2 is not equal to (AC)^2, the Pythagorean theorem does not hold true for this triangle.
Therefore, the buildings do not form a right triangle.

Answer 2

The angle between building 1 and building 3 at building 2 is not a right angle, and hence, the buildings do not form a right triangle.

Explanation: