KL is 7.
Since LMN~XYZ, that means m∠N = m∠Z.
Since the angles are the same, we also know that
sin N = sin Z
Sine is the ratio of the opposite side to the hypotenuse of a right triangle. The sine of N would be the ratio of sides LK to LN, and the sine of Z would be the ratio of sides XW to XZ. That gives us:
x/28 = 3/12
Cross multiply the proportion:
12*x = 28*3
12x = 84
Divide both sides by 12:
12x/12 = 84/12
x = 7
