cutting methods - angled deck joists

[Nearlyman]

It's like this: I don't want to cut a mitre, but I do want to cut a 60 deg angle (a bevel, say) on each end of several 4"x2" joists across the joist ends across its thickness. The joists sit at an angle to the main deck frame which - unlike most conventional decks - has a footprint in the form of an equilateral triangle. Why? The site has been chosen because it is in a corner of the garden, which faces due South. Unhappily, due to the layout of properties on the development, the garden plot, overall, has no right angles to the rear of the house: one corner has an open angle (about 100 deg) and the opposite corner (in the sun) has an acute, included angle, of 62 deg formed by the 1.8M high boundary fencing. I have designed a small, unobtrusive, triangular deck to provide a sunny, slightly raised area, i.e just off the ground, on concrete piers, to take advantage of early morning sunshine - when it is available. The rear of the house close to the building remains in deep shadow until well after midday during the Summer's sunny months.
My 'A' frame has cross beams (joists) which meet the side frames at an angle of 60 deg: the deck boards will be skewed to give a good visual effect: I tested this out using Google Sketch-Up to check.
This then is the issue: what is the most efficient and accurate way, i.e. the best method/ technique, to produce the required angle across the joist ends so that the pitching of the joists remains fixed, i.e constant, thus eliminating or at least reduce the need for 'bespoke' noggins to fit between them? What machine or other "aid" would enable me to achieve this (on site), bearing in mind some of these joists will be up to 3 meters long and weigh quite a bit too! I have already built a 13' x 12', floating deck against the house, (last Summer), but 'square' was easy compared to this challenge! Any practical advice would be much appreciated - thank you.

[greggy]

the machine you are wanting is called.. a compound mitre saw.
bsicaly its a chop saw that not only will cut angles up & down left to right but also diagonly too.

[Nearlyman]

[quote="greggy"]the machine you are wanting is called.. a compound mitre saw.
bsicaly its a chop saw that not only will cut angles up & down left to right but also diagonly too.[/quote]

Thank you - 1) For the solution 2) for understanding the problem.
Indeed I did end up using such a machine and was able to complete over half the task even though the joist section was at the top end of the particular machine's capability. Unfortunately it wasn't up to cutting the deck boards, which were much wider than the joists, as there was no cross cutting feature in the model of chop saw I had loan of. :)