Find the tangent of \angle R .

Step 1: Prove a similarity between the two triangles by using the theorems.
NOTE: The AA Similarity Theorem states that two triangles are similar
if two angles of one triangle are congruent to
two angles of the other triangle.
EXAMPLE: \angle R=\angle W ( since angles with matching arcs are congruent.)
\angle S=\angle U=90
Therefore, by the AA Similarity Theorem, △RST ~ △WUV
Step 2: Find the unknown lengths of the triangle by using the similarity property.
NOTE: Ratios of corresponding side lengths are equal.
EXAMPLE: \frac{ST}{RS}=\frac{UV}{UW}...............(1)
Step 3: Recall the tan definition.
DEFINITION: The tangent (tan) of an angle in a right triangle is a ratio. It is the length of the oppositeleg (opp) divided by the length of the adjacent leg (adj).
EXAMPLE: \tan=\frac{opp}{adj}=\frac{ST}{RS}
= \frac{UV}{UW} [since equation(1)]
= \tan\ R=\frac{20}{21}