If you’re trying to build a house north of an old pine forrest (∼50m tall trees). How far north must you be from the edge of the forrest in order to ensure that you see at least a bit of the Sun even during the winter solstice?
To determine how far north you must be from the edge of the forest to ensure visibility of the Sun during the winter solstice, we need to take into account the angle of the Sun's altitude and the height of the trees.
Step 1: Determine the angle of the Sun's altitude during the winter solstice.
During the winter solstice, which occurs around December 21st each year, the Sun's altitude at noon is at its lowest in the Northern Hemisphere. To find the exact angle, we can consult online resources or use planetarium software to get precise data. However, as a general reference, we can assume the angle to be around 23.5 degrees.
Step 2: Calculate the distance from the edge of the forest.
Now, let's consider the trees in the forest. With an approximate height of 50 meters, we can use simple trigonometry to determine the distance from the edge of the forest by using the tangent function.
tan(angle) = opposite/adjacent
In this case, the opposite side is the height of the trees (50 meters) and the adjacent side is the distance we need to calculate.
Using tangent:
tan(23.5 degrees) = 50 meters/adjacent
Step 3: Solve for the adjacent side.
Rearranging the equation, we get:
adjacent = 50 meters/tan(23.5 degrees)
Calculating the value, we find:
adjacent ≈ 114.47 meters
Therefore, you would need to be at least approximately 114.47 meters north of the edge of the forest to ensure that you see at least a bit of the Sun even during the winter solstice.