Known Height and Shadow Length: If you already know the height of the object (H) and the length of its shadow (S) cast on a flat surface, you can use the following simple formula to calculate the distance to the light source (D):
D = H / tan(A)
where A is the angle of elevation between the horizon and the light source.
This formula assumes the object, the shadow, and the surface are forming a right-angled triangle, with the light source angle (A) being the angle opposite to the height (H).
Known Shadow Length and Distance to Light Source: In some cases, you might know the length of the shadow (S) and the distance from the object to the light source (D). To find the object's height (H), you can use the following formula:
H = D * tan(A)
This formula again uses basic trigonometry to find the height (H) of the object.
It's important to note that these calculations work best when the ground is flat and level, the object's base is on the same plane as the shadow, and the light source is sufficiently far away to be considered a point source. Additionally, the accuracy of these estimations depends on the precision of the measurements and the assumptions made about the geometric relationships involved.
If you're estimating the height of a building or a tall structure, keep in mind that factors such as uneven ground, the angle of the object's base, and the object's complex geometry can introduce errors into the estimation.
Overall, while shadows can provide a rough estimation of an object's height or the height of its surroundings, they should not be relied upon for precise measurements. For accurate measurements, it's best to use other methods such as direct measurements or using specialized equipment like rangefinders or laser distance meters.