Given a trapezoid like the one shown below, how do I determine the length of the wider base? I'm looking for a formula based method rather than drawing the shape and measuring it.

Given a trapezoid like the one shown below, how do I determine the length of the wider base? I'm looking for a formula based method rather than drawing the shape and measuring it.

Use the Law of Sines on the triangles (separately) on either end.
For example, on the right side of the trapezoid, drop a perpendicular from the top right vertex. Call the length of the base of the resulting right triangle $x$. The other (non-hypotenuse) side is 3/4. The bottom (interior) angle is $70^\circ$ while the top (interior) angle is $20^\circ$.
The Law of Sines says $${{3\over 4}\over \sin(70^\circ)}={x\over \sin(20^\circ)}.$$ Solve for $x$ to obtain $x={3\over 4}\cdot{\sin(20^\circ)\over \sin(70^\circ)}\approx 0.272978$.
Play the same game on the other side and you will know the total length of the base of the trapezoid.