Question

the sun casts a shadow on a building and a flagpole. the building is 100 feet tall and it’s shadow is 25 feet the flagpole has a shadow of 5 feet the two triangles shown are similar

Answer 1

From the statement, we know that the two triangles shown are similar. When two triangles are similar, it is true that their corresponding sides are in the same ratio:

$\frac{a}{a^{\prime}}=\frac{b}{b^{\prime}}=\frac{c}{c^{\prime}}$

So, in this case, we have:

$\begin{gathered} a=\text{ ?} \\ b=5ft \\ a^{\prime}=100ft \\ b^{\prime}=25ft \end{gathered}$$\begin{gathered} \frac{a}{a^{\prime}}=\frac{b}{b^{\prime}} \\ \text{ Replace the known values} \\ \frac{a}{100ft}=\frac{5ft}{25ft} \\ \frac{a}{100ft}=\frac{5}{25} \\ \text{ Multiply by 100ft from both sides of the equation} \\ \frac{a}{100ft}\cdot100ft=\frac{5}{25}\cdot100ft \\ a=\frac{5}{25}\cdot100ft \\ \boldsymbol{a=20ft} \end{gathered}$

Therefore, the flagpole measures 20 feet, and the correct answer is option B.