A building 230 feet tall casts a 100 foot long shadow. If a person looks down from the top of the building, what is the measure of the angle between the end of the shadow and the vertical side of the building

From the definition of the tangent:

tan(\theta) = \frac {100}{230} = 0.435

You solve for theta.

\theta = tan^{-1}(0.435) = arctan(0.435)