Step 1. Gather the information that we have and make a diagram.
The length of the ladder is 14 ft, the distance from the base of the ladder to the building is 6 ft and the height of the building is unknown.
We will call this unknown height ''a''.
The following diagram represents the situation:
Step 2. The triangle formed between the floor, the building, and the ladder is a right triangle (it has a 90° angle), this means that we can use the Pythagorean theorem to solve this and find ''a''.
The Pythagorean theorem is represented by the equation:

where a and b are the legs of the triangle, and c is the hypotenuse of the triangle (the side opposite to the 90° angle)
In our case,

And we need to find a.
Step 3. Substituting the known values into the Pythagorean theorem:

Solving the exponential terms:

And solving for a^2 by subtracting 36ft^2 to both sides of the equation:

Taking the square root of both sides and simplifying:
![\begin{gathered} \sqrt[]{a^2}=\sqrt[]{160ft^2} \\ \\ a=\sqrt[]{16\cdot10}ft \\ \\ a=4\sqrt[]{10}ft \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/p1hu3rtfhoec29vsnh1ylu6h2b99zusyhx.png)
This result can also be represented as a decimal number:
![a=4\sqrt[]{10}ft\approx12.65ft](https://img.qammunity.org/2023/formulas/mathematics/college/60ybyacu692lk96rp778w6jeduh015p38f.png)
Answer:
The height of the building is
![4\sqrt[]{10}ft](https://img.qammunity.org/2023/formulas/mathematics/college/nlxxtt6fbbqf4wauy1fox7tz1hialqtkez.png)
The height of the building is approximately
