In order to calculate the effect of tree shading on a roof, we need to know:
- The angle from the roof to the top of the tree at local noon (the sun must be higher than this to cast no shadow)
- The angle from the corners of the roof to the tree and the angle to the top of the tree from the corner.
- Solar altitudes and azimuths during the day.

The first two calculations are simple trig, the last can be obtained from tables.
## The case of Lakeside Court

(see crude drawing at bottom)
Calculating the shadow of a tree on a roof (Assuming a pyramidal shaped tree)

Tree Height 50

Tree distance 25

Roof Height 10

The Noon Angle is merely the Acrtan of the differences in height/ distance= arc tan 1.01 or in degrees 58.

Unfortunately, the tree is not pyramidal, but branches out. As far as we can tell, the maximum extent is about 25 feet up and stick out about 13 feet. This leads to a shadow angle of about 52 degrees.

Corner angle of shade

Distance to tree 25

Distance from N-S 15

Artan 0.54 or in degrees 31 (from South, or 149 degrees)

Elevation angle at the corner is

tree height 35

tree distance 29

Arctan 0.80 or an elevation in degrees of 40

## Conclusion:

From the following tables, we can see that from late March to mid September, the sun is above the critical value of 50 degrees. For late September until the leaves fall, there will be some shading in the late morning and until a little after noon.
To make these estimates more precise we need to confirm the height of the tree and examine its shape more carefully. It seems that with more precise measurements, we probably should not plan on using the garage.

The best way to understand the solar angles is to consider solar elevation by solar azimuth. These are derived from hourly tables of azimuths and elevations.

The solar elevations by hour by month are taken from tables:

And the solar azimuths by hour and month also are tabled:

The basic assumptions are shown as below (but not to scale):