To determine if the triangle with sides 28 meters, 36 meters, and 45 meters is a right triangle, we can use the Pythagorean theorem. This theorem states that in a right triangle, the square of the length of the longest side (hypotenuse) is equal to the sum of the squares of the lengths of the other two sides.
Let's first identify the longest side, which is 45 meters. Now, we will check if the following equation holds true:
\[ a^2 + b^2 = c^2 \]
where \(a\) and \(b\) are the lengths of the two shorter sides (28 meters and 36 meters), and \(c\) is the length of the longest side (45 meters).
Calculating the squares of the sides:
\[ a^2 = 28^2 = 784 \] \[ b^2 = 36^2 = 1296 \] \[ c^2 = 45^2 = 2025 \]
Now, we add \(a^2\) and \(b^2\):
\[ a^2 + b^2 = 784 + 1296 = 2080 \]
Now, we compare \(a^2 + b^2\) with \(c^2\):
\[ 2080 \neq 2025 \]
Since \(a^2 + b^2\) does not equal \(c^2\), the triangle with sides 28 meters, 36 meters, and 45 meters is not a right triangle.