6.  Calculate the unknown length.

Solution:

step 1.  find triangle #1

step 2.  label known & needed

step 3.  select rule = use SIN

step 4.  sin angle = opp / hyp

            sin 12 = 1.775 / hyp

            hyp = 8.53727

step 5.  find triangle #2

step 6.  label known & needed

step 7.  select trig rule = use TAN

step 8.  tan angle = opp / adj

            tan 12 = 0.875 / adj

            adj = 4.1165

step 9.  find length of unknown

hyp from triangle #1 – adj from triangle #2 + 1/2 of diameter of rounded end

8.53727 – 4.1165 + (1/2 x 3.550)= 6.19577”