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}