The above mensuration formula I cribbed from the CRC is, strictly speaking, not a geometric solution to the problem because, in general, the required sine of an angle is often an irrational number which cannot be constructed with drafting tools. However, you can get a solution to the level of precision of your sine tables or your pocket calculator, so for all practical purposes it is a mathematically valid solution (i.e., it is not merely a "rule of thumb" answer).

Does anyone know if the CRC (Chemical Rubber Company Handbook of Mathematical Tables and Formulae) is still published? It's probably obsolete now in this age of pocket calculators and the internet, but it used to be the student's best friend during the slide rule era. It contained trig and log tables, derivatives and integrals, identities, summaries of essential math formulae and procedures, and many other useful items. No one uses trig tables any more, and no one these days even knows what log tables are used for!

It was available in a phonebook-sized desk edition which contained all sorts of arcana (like the boiling point of liquid Hafnium or the refractive indices of industrial glasses), and an abridged and more portable briefcase-sized edition. After using one for a while, you developed an uncanny intuition for locating stuff. It was the information technology of the time. I still use my 1964 edition once a year or so, in cases like this one.