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:

`(a)/(a^(\prime))=(b)/(b^(\prime))=(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} (a)/(a^(\prime))=(b)/(b^(\prime)) \\ \text{ Replace the known values} \\ (a)/(100ft)=(5ft)/(25ft) \\ (a)/(100ft)=(5)/(25) \\ \text{ Multiply by 100ft from both sides of the equation} \\ (a)/(100ft)\cdot100ft=(5)/(25)\cdot100ft \\ a=(5)/(25)\cdot100ft \\ \boldsymbol{a=20ft} \end{gathered}`

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