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 CALCULATING SUN ANGLE

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 formula is:

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