At 3:00 PM a man 148 cm tall casts a shadow 143 cm long. At the same time, a tall building nearby casts a shadow 170 m long. How tall is the building?
148 / 143 = x / 170 m
To find the height of the building, we can set up a proportion using the height and shadow length of the man and the building.
Let's assume:
Height of the building = h
Shadow length of the building = s
The proportion can be written as:
(man's height) / (man's shadow length) = (building's height) / (building's shadow length)
Substituting the given values:
148 cm / 143 cm = h / 170 m
Now, let's solve for h (height of the building):
148 cm * 170 m = 143 cm * h
25,160 cm.m = 143h cm
To convert both sides to the same unit (either meters or centimeters), we need to convert 25,160 cm.m to the same unit as 143h cm.
1 m = 100 cm
25,160 cm.m = 25,160 cm / 100 cm = 251.6 m
Now we can solve for h:
251.6 m = 143h cm
Divide both sides by 143:
251.6 m / 143 = h
h ≈ 1.760 cm
Therefore, the height of the building is approximately 1.760 cm.
To find the height of the building, we can use a proportion. The ratio of the man's height to his shadow length should be equal to the ratio of the building's height to its shadow length.
Let's assign variables to the unknowns. Let's assume the height of the building is "h" meters. We already know the length of the building's shadow is 170 m.
So, we can set up a proportion:
148 cm / 143 cm = h m / 170 m
To solve this proportion, we need to convert the units to the same system. Let's convert the man's height and shadow length to meters since the building's measurements are in meters.
148 cm = 1.48 m (divide by 100)
143 cm = 1.43 m (divide by 100)
Now, let's substitute the values into the proportion:
1.48 m / 1.43 m = h m / 170 m
To find the value of "h", we can cross-multiply and then divide:
1.48 m * 170 m = 1.43 m * h m
250.6 m = 1.43h
To solve for "h", we need to isolate it. Divide both sides of the equation by 1.43:
250.6 m / 1.43 = h
The height of the building is approximately 175.35 meters.