Question

What is the height of the building pictured below if its shadow is 100 ft. long?

Answer 1

Yeah.. baby, do the SOH CAH TOA with the hula hoop

$\bf sin(\theta)=\cfrac{opposite}{hypotenuse} \qquad \qquad % cosine cos(\theta)=\cfrac{adjacent}{hypotenuse} \\ \quad \\ % tangent tan(\theta)=\cfrac{opposite}{adjacent}$

so.. hmmm we have in the picture, an angle, and two sides,
actually, is the "adjacent" side, and the "opposite"

so.. which  of those ratios give us only
the angle
the adjacent side
the opposite side?

ahhha!, is Ms tangent
so  $\bf tan(\theta)=\cfrac{opposite}{adjacent}\implies tan(42^o)=\cfrac{h}{100}$

solve for "h"