METEOROLOGIST JEFF HABY
The length of a shadow depends on the sun angle. If the sun is directly overhead then there is
no shadow cast. As the sun gets closer to the horizon the shadow length increases. Below is an
example problem that shows how to calculate sun angle given the height of the object and the
length of the shadow cast.
Example: A storm has a height of 8,000 m and casts a 2,000 m shadow. What is the sun angle?
Assume a storm and the shadow cast make a right triangle. Since it is a right
triange there is a formula that can used to find the angle since two sides are known. The
tan(angle) = opposite / adjacent
The opposite side (height of storm) is the 8,000 m height. The shadow length of the adjacent side
is 2,000 m. What is the sun angle? use a scientific calculator that has trig functions
tan(angle) = 8,000/2,000
tan(angle) = 4
angle = tan^-1(4)
angle = 76 degrees sun angle above horizon
The same calculation process can be done using smaller objects such as placing a pole in the ground and measuring
pole height and shadow length to find sun angle.
For example, suppose a pole has a height of 3 feet and the shadow cast is 6 feet. Below is the
sun angle calculation:
tan(angle) = 3 feet / 6 feet
tan(angle) = 0.5
angle = tan^-1(0.5)
angle = 27 degrees sun angle above horizon