In a right triangle with a hypotenuse length of 746 feet and one side measuring 524 feet, what is the length of the other side?

In a right triangle, the relationship among the lengths of the sides is defined by the Pythagorean theorem. This theorem states that the sum of the squares of the two legs (the sides forming the right angle) is equal to the square of the hypotenuse (the side opposite the right angle).

In this case, the length of the hypotenuse is provided as 746 feet, and one of the legs is given as 524 feet. To find the length of the other side, we can set up the equation based on the Pythagorean theorem:

Let the length of the unknown side be denoted as ( x ). The equation can be formulated as follows:

( 524^2 + x^2 = 746^2 )

Calculating the squares:

• For the hypotenuse: ( 746^2 = 556756 )

• For the known side: ( 524^2 = 274576 )

Now substituting these values into the Pythagorean theorem equation:

( 274576 + x^2 = 556756 )

To isolate ( x^2 ), we need to subtract ( 274576 ) from both sides:

( x^2