In today's earlier post I explained how to calculate the dihedral angle of a roof hip under the conditions that the eaves of the adjacent roof surfaces that form the hip meet at 90º from the plan view perspective. Now for the more universal method of calculating this dihedral hip angle by hand. This method can be used to calculate any dihedral hip or valley angle for any two adjacent roof surfaces. Warning! This is some serious nerd-worthy content.
To save time I am referring you all to a write up I authored back in 2011 on a sheet metal workers' focused forum. Posts #8 and #9 explain this quite well. I used to watch this forum years ago as I learned and shared different ideas for fabricating and installing architectural sheet metal. There are many other highly skilled tradesmen that would contribute to the content on that forum.