This problem can be solved using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be written as: a² + b² = c².

In this case, the northbound train has traveled 55 miles (this is one side of the triangle), the eastbound train has traveled a distance we'll call 'x' (this is the other side of the triangle), and the straight-line distance between the two trains is 73 miles (this is the hypotenuse of the triangle).

So, we can set up the equation as follows:

55² + x² = 73²

Solving for 'x' gives us the distance the eastbound train has traveled.

First, square the known values:

3025 + x² = 5329

Subtract 3025 from both sides to isolate x²:

x² = 5329 - 3025
x² = 2304

Finally, take the square root of both sides to solve for 'x':

x = √2304
x = 48

So, the eastbound train has traveled 48 miles.

Question

This problem can be solved using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be written as: a² + b² = c².

In this case, the northbound train has traveled 55 miles (this is one side of the triangle), the eastbound train has traveled a distance we'll call 'x' (this is the other side of the triangle), and the straight-line distance between the two trains is 73 miles (this is the hypotenuse of the triangle).

So, we can set up the equation as follows:

55² + x² = 73²

Solving for 'x' gives us the distance the eastbound train has traveled.

First, square the known values:

3025 + x² = 5329

Subtract 3025 from both sides to isolate x²:

x² = 5329 - 3025
x² = 2304

Finally, take the square root of both sides to solve for 'x':

x = √2304
x = 48

So, the eastbound train has traveled 48 miles.

Knowee AI · Accepted Answer