Question

t a certain time of day, a 5 foot tall man has a 7.5 foot shadow. If a tree is 20 feet tall, what is the length of the shadow of the tree?

A. 30 feet
B. 12 feet
C. 24 feet
D. 15 feet

Answer 1

if you take a peek, the same angle the "man" makes, the "tree" makes

what's that angle?
well
$$
sin(\theta) = \cfrac{opposite}{hypotenuse}\\
\text{so for the "man"}\\
sin(\theta) = \cfrac{5}{7.5}\\
\text{that gives you its sine value, arcsine that}\\
sin^{-1}\pmatrix{sin(\theta)} = sin^{-1}\pmatrix{\cfrac{5}{7.5}}\\
$$