Missed! just.

When, having survived another night, I throw open the front door to greet the day, the foreground of the view is largely occupied by a mighty ash tree Fraxinus excelsior at the bottom of the yard. Over 25 years under our care, it has grown a lot. It's a pity we had not the foresight to measure it back in 1996, when for two pins we could have chopped down its scrubby ass for firewood. The only thing to say is "My, haven't you grown?" which is patronising and not very quantitative. It is so tall that I have anxed, with Bishop Berkeley: "if a tree falls in the yard and there's nobody to hear, will it make a noise . . . as it smashes the windows of the house". A year ago, I did some guesstimating to calculate that a) the tree was 8.5 times taller that the adjacent 2016 woodshed b) that was quite enough to come knocking on (or through!) the front door . . .  roughly.

Two Sundays ago we had brilliant sunshine after lunch and, as I stood <burping quietly> on the stoop, it was clear that the shadows of the topmost twigs almost grazed the edge of the front door-step. Oh ho, I thought, as I slapped a trigonometry hat on my pointy head, if I knew what was the angle of altitude of the sun on this day at this time in Ireland then tan(x)= opposite/adjacent would tell me whether the vertical tree is taller than the distance to the door if it fell this way? 

So I looked it up
Time: 1406 3rd April any year
Altitude: 41°
Direction 193° SSW
as tan(41°) = 0.869 then the shadow must be longer than the vertical tree and therefore we are safe from tree-fall for this year. In pictures:

In fact, with the way the conundrum is structured, any angle less than 45° will be okay and any angle greater than 45° is a potential problem. All that talk about trigonometry and tan(x) was a big red herring! With ash-dieback scourging through the local trees and with the tree in question definitely symptomatic last year, we don't have to worry about the tree getting much taller. If there is an Easterly gale then all bets are off for the slated shed next door . . . and the car, which we always park between tree and shed, will have to take its chances.