The astrolabe or sextant was designed to perform said measurements. GPS is common, cheap and easy to use, and it has displaced the units. These tools of navigation are now inexpensive and easy to come by. (Kind of like slide rules after electronic calculators became common.) A look on eBay will probably reveal several different units in a range of prices.
Use the link to the Wikipedia article on the sextant and see what it can do.
To calculate the precise location of the sun, see the following site: http://www.astro.uio.no/~bgranslo/aares/calculate.html
For an on-line calculator in JavaScript check here: http://www.learn.londonmet.ac.uk/packages/daymedia/axel/sky/sunpath_calc.html