Choice B is correct. It's given that right triangle $R S T$ is similar to triangle $U V W$ , where $S$ corresponds to $V$ and $T$ corresponds to $W$ . It's given that the side lengths of the right triangle $R S T$ are $upper R upper S equals 20$ , $upper S upper T equals 48$ , and $upper T upper R equals 52$ . Corresponding angles in similar triangles are equal. It follows that the measure of angle $T$ is equal to the measure of angle $W$ . The hypotenuse of a right triangle is the longest side. It follows that the hypotenuse of triangle $R S T$ is side $T R$ . The hypotenuse of a right triangle is the side opposite the right angle. Therefore, angle $S$ is a right angle. The adjacent side of an acute angle in a right triangle is the side closest to the angle that is not the hypotenuse. It follows that the adjacent side of angle $T$ is side $S T$ . The opposite side of an acute angle in a right triangle is the side across from the acute angle. It follows that the opposite side of angle $T$ is side $R S$ . The tangent of an acute angle in a right triangle is the ratio of the length of the opposite side to the length of the adjacent side. Therefore, $\tan T = \frac{R S}{S T}$ . Substituting $20$ for $R S$ and $48$ for $S T$ in this equation yields $\tan T = \frac{20}{48}$ , or $\tan T = \frac{5}{12}$ . The tangents of two acute angles with equal measures are equal. Since the measure of angle $T$ is equal to the measure of angle $W$ , it follows that $\tan T = \tan W$ . Substituting $\frac{5}{12}$ for $\tan T$ in this equation yields $\frac{5}{12} = \tan W$ . Therefore, the value of $\tan W$ is $\frac{5}{12}$ .

Choice A is incorrect. This is the value of $\sin W$ .

Choice C is incorrect. This is the value of $\cos W$ .

Choice D is incorrect. This is the value of $StartFraction 1 Over tangent upper W EndFraction$ .