Explain how you could use shadows and similarity to find the height of a building.?

Question

I tried to find an explanation in the book and couldn't, so don't waste your breath telling me to do my own homework.

Answer 1

It's a simple proportion. Let's say I'm 5 ft tall and my shadow at the moment is 4 feet tall. I can't measure a building, but I can measure its shadow. Let's say the shadow is 15 feet. So, I set it up as 4/5=15/x
Cross multiply and you get 15*5=4x
15*5=75. so, 4x=75. Divide the whole thing by 4 to isolate x and x=18 and 3/4

Answer 2

The building makes a 90 degree angle with the ground.
Set up a pole at 90 degrees with the ground, in the sun.
Measure the pole from top to ground, then measure its shadow.
Immediately (before the sun moves and makes the shadows change) measure the length of the building's shadow.
The ratio of the height of the pole to the length of its shadow will equal the ratio of the height of the building to the length of its shadow.
Hp/Sp = Hb/Sb
You know all values except Hb (Height of building), so solve for Hb.

Answer 3

Ratios are the key here. If you know the height of an object and measure its shadow length, that ratio is the same as for any object in the area, assuming a flat surface for the shadow.
If you are 6 feet tall, and your shadow is 3 feet long, then a building whose shadow is 20 feet long must be 40 feet high.