The angle of elevation from the top of a 95 -foot tall building to a hot air balloon in the sky \( 76^{\circ} \). If the horizontal distance between the building and the hot air balloon is 354 feet, find the height of the hot air bailoon.

To find the height of the hot air balloon, we can use trigonometry. From the top of the building, we can set up the equation involving tangent, which is the ratio of the opposite side (the height of the hot air balloon minus the height of the building) to the adjacent side (the horizontal distance). First, calculate the height difference using the tangent of the angle of elevation: \[ \tan(76^\circ) = \frac{h - 95}{354} \] Now, we can solve for \(h\): \[ h - 95 = 354 \cdot \tan(76^\circ) \] \[ h = 354 \cdot \tan(76^\circ) + 95 \] Calculating \( \tan(76^\circ) \) gives approximately \( 4.010 \), so: \[ h = 354 \cdot 4.010 + 95 \approx 1425.54 + 95 \approx 1520.54 \] Thus, the height of the hot air balloon is approximately \( 1520.54 \) feet. Enjoy floating high in the sky!