Question

when the sun is at a certain angle in the sky, a 20 - foot flagpole will cast a 16 - foot shadow. how tall is a person if he casts a 4.4 - foot shadow at the same time? the person is ______ feet tall. enter only the number. the solution is

Explanation:

Step1: Set up the proportion

Since the ratio of height to shadow length is the same for both the flagpole and the person, we can set up the proportion \(\frac{\text{height of flagpole}}{\text{shadow of flagpole}}=\frac{\text{height of person}}{\text{shadow of person}}\). Let \(h\) be the height of the person. So, \(\frac{20}{16}=\frac{h}{4.4}\).

Step2: Cross - multiply and solve for \(h\)

Cross - multiplying gives us \(16h = 20\times4.4\). First, calculate \(20\times4.4=88\). Then, \(h=\frac{88}{16}\). Simplifying \(\frac{88}{16}=\frac{88\div8}{16\div8}=\frac{11}{2}=5.5\).

Answer:

\(5.5\)