A 50-foot flagpole is at the entrance of a building that is 300 feet tall. If the length of the flagpole's shadow is 30 feet at a certain time of day, how long is the building's shadow at that time?
Answers
Answer:
180 feet
Step-by-step explanation:
Given: A 50-foot flagpole is at the entrance of a building that is 300 feet tall.
Them two right triangles must be formed by flagpole and building with the ground and are similar because the angle of the sun is the same at the same time of day.
So by the properties of similar triangles,
1) All the three angles of each triangle must be equal to a corresponding angle of the other triangle.
2) Sides are proportional to the corresponding sides in the other triangle,
\begin{gathered}\frac{\text{height of flagpole}}{\text{ length of flagpole's shadow }}=\frac{\text{height of building}}{\text{length of building's shadow}}\\\\\Rightarrow\frac{50}{30}=\frac{300}{\text{length of building's shadow}}\\\\\Rightarrow\text{length of building's shadow}=\frac{300\times3}{5}\\\\\Rightarrow\text{length of building's shadow}=180\end{gathered}
length of flagpole’s shadow
height of flagpole
=
length of building’s shadow
height of building
⇒
30
50
=
length of building’s shadow
300
⇒length of building’s shadow=
5
300×3
⇒length of building’s shadow=180
Therefore, the length of building's shadow is 180 feet.
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