Question

A building casts a shadow of 30 feet. At the same time, a person who is 5 feet tall casts a shadow that is 2 feet long.

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image.png

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How tall is the building?

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feet

Answer 1

To find the height of the building, we can use the property of similar triangles. The height of the building and the length of its shadow form one triangle, while the height of the person and the length of their shadow form another triangle.

Let:
- \( h \) be the height of the building.
- The height of the person is 5 feet.
- The shadow of the building is 30 feet long.
- The shadow of the person is 2 feet long.

From the similar triangles, we can set up the following proportion:

\[
\frac{h}{30} = \frac{5}{2}
\]

Now, we can cross-multiply to solve for \( h \):

\[
2h = 5 \times 30
\]

\[
2h = 150
\]

Now, divide both sides by 2:

\[
h = \frac{150}{2} = 75
\]

Therefore, the height of the building is **75 feet**.