Marta is standing 4ft. Behind a fence 6 inches tall. When she looks over the fence, she can just. See the top of a building. She knows that the building is 32 ft. 6 inches behind the fence. Her eyes are 5 ft. From the ground. How tall is the building?

Read what you wrote.

That's a might small fence.

To determine the height of the building, we can use the concept of similar triangles.

First, let's visualize the situation:

Marta's line of sight forms a right triangle with the height of the fence and the height of the building. The distance from the fence to the building creates another right triangle with the same height of the fence.

Let's assign variables to the unknown heights. Let "h" represent the height of the building and "x" represent the height of the fence.

Using the properties of similar triangles, we can set up the following ratio:

(h + x) / h = (5 + x) / 5

Now, let's substitute the given values:

(x + 6) / h = (5 + x) / 5

Cross-multiplying, we get:

5(x + 6) = (5 + x)h

Expanding the equation:

5x + 30 = 5h + xh

Since we know the distance from the fence to the building (32 ft. 6 inches), which is an additional 4 ft. behind the fence:

x + 6 + 4 = x + 10

Substituting this into the equation:

5(x + 10) = (5 + x)h

5x + 50 = 5h + xh

Simplifying the equation:

50 = xh

We also know that the distance from the fence to the building is 32 ft. 6 inches, which can be converted to 32.5 ft:

xh = 32.5

Now we can solve for x and h simultaneously:

50 = xh
32.5 = xh

By substituting the second equation into the first, we get:

50 = 32.5

Solving for x:

x ≈ 0.65 ft

Now we can find the height of the building using the second equation:

32.5 = 0.65h

Solving for h:

h ≈ 50 ft

Therefore, the height of the building is approximately 50 feet.