Question

a cedar tree that is 8 feet tall casts a shadow 15 feet long. if a nearby marble column casts a shadow 30 feet long, what is the marble column’s height? write your answer as a whole number or a decimal. do not round. feet

Explanation:

Step1: Set up proportion

Since the ratio of height to shadow - length is the same for both the tree and the column, we can set up the proportion $\frac{h_1}{s_1}=\frac{h_2}{s_2}$, where $h_1 = 8$ feet (height of the tree), $s_1 = 15$ feet (shadow - length of the tree), $h_2$ is the height of the column, and $s_2 = 30$ feet (shadow - length of the column). So, $\frac{8}{15}=\frac{h_2}{30}$.

Step2: Solve for $h_2$

Cross - multiply: $15h_2=8\times30$. Then $15h_2 = 240$. Divide both sides by 15: $h_2=\frac{240}{15}$.

Step3: Calculate the value of $h_2$

$h_2 = 16$.

Answer:

16