A flagpole $95.8 \mathrm{ft}$ tall is on the top of a building. From a point on level ground, the angle of elevation of the top of the flagpole is $35.5^{\circ}$, while the angle of elevation of the bottom of the flagpole is $25.5^{\circ}$. Find the height of the building. The building is about yt tall. (Round to the nearest foot as needed.)

Step 1 ：Given that the height of the flagpole is 95.8 ft, the angle of elevation to the top of the flagpole is 35.5 degrees, and the angle of elevation to the bottom of the flagpole is 25.5 degrees.

Step 2 ：We can use the tangent of an angle in a right triangle, which is the ratio of the opposite side to the adjacent side, to set up two equations.

Step 3 ：Let's denote the height of the building as \(h_{building}\) and the distance from the point on the ground to the building as \(d\).

Step 4 ：From the angle of elevation to the top of the flagpole, we have \(\tan(35.5^{\circ}) = \frac{h_{building} + 95.8}{d}\).

Step 5 ：From the angle of elevation to the bottom of the flagpole, we have \(\tan(25.5^{\circ}) = \frac{h_{building}}{d}\).

Step 6 ：We can solve these two equations to find \(d\) and \(h_{building}\).

Step 7 ：By calculation, we find that \(d\) is approximately 134.31 and \(h_{building}\) is approximately 64.06.

Step 8 ：Rounding to the nearest foot, the height of the building is approximately 64 feet.

Step 9 ：Final Answer: The height of the building is \(\boxed{64}\) feet.