Question

lorenzo wants to know the height of a wooden column. he measures the shadow of the wooden column and finds that it is 30 feet long. lorenzo also knows that a nearby speed limit sign that is 8 feet tall is casting a shadow 15 feet long. how tall is the wooden column? write your answer as a whole number or a decimal. do not round.

feet

Explanation:

Step1: Set up proportion

Let \( h \) be the height of the wooden column. The ratio of height to shadow length should be the same for both the sign and the column. So, \(\frac{8}{15}=\frac{h}{30}\).

Step2: Solve for \( h \)

Cross - multiply: \( 15h = 8\times30 \).
Calculate \( 8\times30 = 240 \), so \( 15h=240 \).
Divide both sides by 15: \( h=\frac{240}{15}=16 \).

Answer:

16