At 3:00 PM a man 146 cm tall casts a shadow 136 cm long. At the same time, a tall building nearby casts a shadow 177 m long. How tall is the building?
Well, let's do some shadowy arithmetic, shall we? If a man who is only 146 cm tall casts a shadow that's 136 cm long, then we can use some proportionality magic to solve this. If the little man's shadow is 136 cm, then for every 1 cm of height, he gets 136/146 cm of shadow. Now let's apply this same logic to the tall building. If its shadow is 177 m long, we can assume that for every 1 m of height, it gets 177/?? m of shadow. Since our unit conversion skills are on point, we know that 1 m = 100 cm, so we just need to find the missing factor of the proportionality, and voila, we'll find the height of the building! But since I'm a clown bot, I might not be the most reliable source for calculations
To solve this problem, we can set up a proportion to find the height of the building.
Let's assign the following variables:
- Man's height: h1 = 146 cm
- Man's shadow length: s1 = 136 cm
- Building's shadow length: s2 = 177 m
We can use the proportion:
h1 / s1 = h2 / s2
where h2 represents the height of the building.
Now, let's substitute the given values into the proportion:
146 cm / 136 cm = h2 / 177 m
To solve the equation, we need to convert cm to m by dividing both sides of the equation by 100:
1.46 / 1.36 = h2 / 177
Simplifying the left side of the equation:
1.0735 ≈ h2 / 177
Next, we can cross-multiply to find h2:
1.0735 * 177 = h2
h2 ≈ 190.1295
Therefore, the height of the building is approximately 190.13 meters.
To find the height of the building, we can set up a proportion comparing the height of the man to the height of the building using their respective shadow lengths.
Let's denote:
h = height of the building (in meters)
Using the given information, we can set up the proportion as follows:
\(\frac{146}{136} = \frac{h}{177}\)
To solve for h, we can cross-multiply and then solve for the unknown variable:
146 * 177 = 136 * h
25742 = 136h
Now, divide both sides of the equation by 136:
\(h = \frac{25742}{136}\)
To find the final answer, calculate the division:
h ≈ 189.25 m
Therefore, the height of the building is approximately 189.25 meters.
146/136 = x/177
136x = 25,842
x = 190 m