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 D = \angle G ( since angles with matching arcs are congruent.)

                                \angle E = \angle H = 90

                 Therefore, by the AA Similarity Theorem, △GHI~△DEF

Step 2: Find the unknown lengths of the triangle by using the similarity property.  

            NOTE: Ratios of corresponding side lengths are equal.

            EXAMPLE: \frac{HI}{GI} = \frac{EF}{DF} ...............(1)

Step 3: Recall the sin definition.

          DEFINITION: The sine (sin) of an angle in a right triangle is a ratio. It is the

                                length of the opposite leg (opp) divided by the length of the  

                                 hypotenuse (hyp).


        EXAMPLE: \sin=\frac{opp}{hyp}=\frac{HI}{GI}

                                               = \frac{EF}{DF}   [since equation(1)]

                                               = \frac{48}{73}