Find all values of $t$ such that $t - 1$, $t + 1$, and $4$ could be the lengths of the sides of a right triangle.

side 1: t - 1

side 2: t + 1

side 3: 4

side 1 + side 2 > side 3   &  side 2 + side 3 > side 1   &  side 3 + side 1 > side 2

(t - 1)   + (t + 1)   >   4              (t + 1)   +   (4)    >   (t - 1)            (4)     + (t - 1)  >  (t + 1)

       2t > 4                                  t + 5          >   t - 1                      t + 3       >   t + 1

         t > 2                                       5 > -1   (TRUE)                            3 > 1 (TRUE)

t > 2

the answer is b.

step-by-step explanation:

by the trigonometric ratio tangent, tangent equals opposite divided by adjacent.

therefore, tan(50) equals ac/3

multiply each side by 3 to get: ac=3tan(50)

the answer is b.