Answer:
Building's shadow length = 180 feet.
Step-by-step explanation:
Given:
A 50-foot flagpole is at the entrance of a building that is 300 feet tall.
Its forms a right angled triangle from both ends,both of them are similar because the angle of the sun is the same at the same time of day.
From similar triangle property we can say that.
⇒ length of the building shadow times height of the flagpole's = length of the flagpole's shadow times height of the building
Or
[tex]\frac{length\ of\ the\ building\ shadow}{height\ of\ the\ building} =\frac{length\of\ the\ flagpole's\ shadow}{height\ of\ the\ flagpole's}[/tex]
Plugging the values in the above equation we have,
Let length of the building shadow ='x' feet
⇒ [tex]\frac{x}{300} =\frac{30}{50}[/tex]
⇒ [tex]\frac{x}{300}\times 300 =\frac{30}{50}\times 300[/tex]
⇒ [tex]x=\frac{300\times 30}{50}[/tex]
⇒ [tex]x=\frac{9000}{50}[/tex]
⇒ [tex]x=180[/tex] feet.
So the length of the building shadow is 180 feet.
