I wonder if tan is short for tangent (relating to right angle triangles -)
What if they mean r.(right) tangent, not "v." - and the angle between the saw mill wharf and the East bluff to the right of the wharf being 79 degrees, and the l.(left) tangent between the saw mill wharf and the West bluff to the left of the wharf being 72 degrees.
I've given these some thought, and I wonder if "tangent" refers to imaginary tangent lines that touch the bluffs at only one point - i.e. a line from the ship to where the bluff appears to "end" (due to curving round past a point). However, I've tried putting in the angles, and the location that comes out is pretty odd, about 2.8 miles away on bearing 305 from the St Paul and Tacoma Mill's Wharf. Even today, there's absolutely nothing there! I also don't get why you'd reference the bluffs rather than Point Brown and Point Defiance, which mark where the "tangents" to the bluffs would be.
The "Sawmill Wharf" may also be open to interpretation - Sawmills popped up on both sides of the bay at various dates, including one at about 400 Schuster Parkway on the Tacoma Side (edit: seems this was dismantled in 1898, however), and also the Gawley Mill indicated on the 1910 map. However, I don't think the angles make much more sense for either of those...