What is the approximate distance between two houses measured by a surveyor using the right triangle with legs of 50 feet and 80 feet?

To determine the distance between the two houses, we can use the Pythagorean theorem, which is applicable to right triangles. According to this theorem, 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 (the legs).

Here, the lengths of the legs are given as 50 feet and 80 feet. We label these lengths as (a) and (b). The hypotenuse (c) can be calculated using the formula:

[ c = \sqrt{a^2 + b^2} ]

Substituting the values of (a) and (b):

[ c = \sqrt{50^2 + 80^2} ] [ c = \sqrt{2500 + 6400} ] [ c = \sqrt{8900} ]

Calculating the square root of 8900:

[ c \approx 94.34 ]

Since we are looking for an approximate distance, we can round this to 94 feet. This matches with the choice labeled as 94 ft. Thus, the distance between