Problem description:
When the sun is at 225 degrees and 270 degrees, what is the angle between the shadow of buildings in Zhengzhou and the ground? Thank you! !
Analysis:
The longitude of the sun is 225 degrees and 270 degrees, which are winter day and winter solstice day respectively.
"The angle between the architectural shadow of Zhengzhou and the ground" is a bit difficult to understand.
You mean the height angle of the sun at noon, right?
For a certain place on the earth, the height of the sun refers to the angle between the incident direction of sunlight and the ground plane. We use h to represent this angle, which is numerically equal to the horizon height of the sun in the celestial horizon coordinate system.
The solar altitude angle varies with local time and solar declination. The declination of the sun is represented by δ, and geographical observation is carried out.
Latitude is expressed by φ, local time (hour angle) is expressed by t, and the solar altitude angle has a calculation formula:
sin h=sin φ sin δ+sin φ cos δ cos t
At sunrise and sunset, the altitude angle of the sun changes constantly in the same place throughout the day. At sunrise and sunset, the angle is zero and positive.
The height angle of the sun is the largest at noon.
The angle at noon is 0, and the above formula can be simplified as:
sin H=sin φ sin δ+sin φ cos δ
Where h stands for the noon sun altitude angle.
From the sum and difference of two angles, the formula of trigonometric function can be obtained.
sin H=cos(φ-δ)
Therefore,
For the northern hemisphere, h = 90-(φ-δ);
For the southern hemisphere, h = 90-(δ-φ).
The latitude of Zhengzhou is about 35 degrees north latitude.
I hope my answer is helpful to you.