What is the distance in inches between the ends of a 6-inch horizontal line and an 8-inch vertical line drawn at right angles?

To determine the distance between the ends of a 6-inch horizontal line and an 8-inch vertical line that are drawn at right angles, we can visualize this scenario as a right triangle.

In this case, the horizontal line represents one leg of the triangle, while the vertical line represents the other leg. The distance between the ends of the lines would be the hypotenuse of this right triangle.

According to the Pythagorean theorem, the length of the hypotenuse can be calculated using the formula:

[

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

]

where (a) is the length of the horizontal line (6 inches), (b) is the length of the vertical line (8 inches), and (c) is the distance between the two ends.

Substituting the values we have:

[

c = \sqrt{(6)^2 + (8)^2}

]

Calculating the squares:

[

c = \sqrt{36 + 64}

]

[

c = \sqrt{100}

]

Therefore,

[

c = 10

]

This results in a distance of 10 inches between the