In the diagram, a building casts a 35-ft shadow and a flagpole casts an 8-ft shadow. If the flagpole is 18 ft tall, how tall is the building? Round to the nearest tenth.

Ms Sue solved the "same" question.

Just change the numbers

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To solve this problem, we can set up a proportion using the similar triangles formed by the building, the building's shadow, the flagpole, and the flagpole's shadow.

Let's denote the height of the building as "x."

According to the given information, the flagpole is 18 ft tall and casts an 8-ft shadow, while the building casts a 35-ft shadow.

Based on the similar triangles, we can set up the proportion:

height of building / length of building shadow = height of flagpole / length of flagpole shadow

Using the given values:

x / 35 = 18 / 8

Now, we can cross-multiply and solve for x:

8x = 35 * 18
8x = 630

Dividing both sides by 8:
x = 630 / 8
x ≈ 78.75

Therefore, the building is approximately 78.75 ft tall, rounded to the nearest tenth.

To solve this problem, we can use proportions.

Let's assume the height of the building is h.

According to the given information:
Height of the flagpole = 18 ft
Length of the flagpole's shadow = 8 ft
Length of the building's shadow = 35 ft

We can set up a proportion using the height and shadow of the flagpole and the building:
(height of flagpole) / (length of flagpole's shadow) = (height of building) / (length of building's shadow)

Substituting the given values:
18 ft / 8 ft = h / 35 ft

To solve for h (the height of the building), we can cross-multiply:
8 ft * h = 18 ft * 35 ft

Now let's calculate that on a calculator:
h = (18 ft * 35 ft) / 8 ft

h ≈ 78.75 ft

Therefore, the height of the building is approximately 78.75 feet when rounded to the nearest tenth.

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