To solve this problem, we can use the concept of similar triangles. The man and the building both cast shadows at the same time, so the angle of elevation of the sun is the same for both. Therefore, the ratios of their heights to the lengths of their shadows are equal.

Let the height of the building be $h$ meters. Here’s the information we have:

• The height of the man is 137 cm (or 1.37 m, since $100 \, \text{cm} = 1 \, \text{m}$).
• The length of the man’s shadow is 138 cm (or 1.38 m).
• The length of the building’s shadow is 161 m.

Using the ratio of height to shadow length for both the man and the building, we get:

$\frac{1.37}{1.38} = \frac{h}{161}$

Now, solve for $h$:

$h = \frac{1.37 \times 161}{1.38}$

Let’s calculate that.

$h = \frac{1.37 \times 161}{1.38} \approx \frac{220.57}{1.38} \approx 159.79 \, \text{m}$

So, the height of the building is approximately 159.79 meters.

Would you like more details on this, or do you have any other questions?

Here are 5 related questions to expand your understanding:

1. How does the concept of similar triangles apply to shadows and heights?
2. What would the height of the building be if the shadow length changed to 180 meters?
3. How would the height change if the man's shadow was only 100 cm long?
4. How do units of measurement conversion (cm to m) affect the final result?
5. Can this method be used at any time of the day? Why or why not?

Tip: Always ensure that all units are consistent (e.g., meters with meters) before setting up ratios in word problems.