Questions: At 3:00 PM a man 137 cm tall casts a shadow 130 cm long. At the same time, a tall building nearby casts a shadow 177 m long. How tall is the building?
Transcript text: At 3:00 PM a man 137 cm tall casts a shadow 130 cm long. At the same time, a tall building nearby casts a shadow 177 m long. How tall is the building?
Solution
Solution Steps
Step 1: Convert units
Convert the building's shadow length from meters to centimeters: 177 m * 100 cm/m = 17700 cm
Step 2: Set up a proportion
Let _h_ be the height of the building. Set up a proportion relating the man's height and shadow length to the building's height and shadow length:
137 cm / 130 cm = _h_ / 17700 cm
Step 3: Solve for _h_
Cross-multiply and solve for _h_:
_h_ = (137 cm * 17700 cm) / 130 cm
_h_ = 18561.538 cm
Step 4: Convert back to meters
Convert the building's height from centimeters to meters:
_h_ ≈ 185.62 m
Final Answer: The building is approximately 185.62 meters tall.