Is a triangle with measures of 6 ft, 21 ft, 23 ft a right triangle

No it is not a right triangle

To see if this possible triangle is a right triangle we have to apply the Pythagorean theorem:

In any right triangle:

hypotenuse²=leg₁²+leg₂²

In this case the possible hypotenuse will be the largest side:

hypotenuse=23 ft

and the sides the legs:

leg₁=6 ft

leg₂=21 ft

Therefore:

hypotenuse = (23 ft) ²=529 ft²

leg₁²+leg₂² = (6 ft) ² + (21 ft) ²=477 ft²

becuse:

hypotenuse² ≠l eg₁²+leg₂²

529 ft²≠477 ft²

This possible triangle is not a right triangle.