The angle of elevation to the top of a building changes from \( 23^{\circ} \) to \( 46^{\circ} \) as an observer advances 155 feet toward the building. Find the height of the building, \( x \), to the nearest foot. The height of the building is approximately \( \square \) feet. (Do not round until the final answer. Then round to the nearest whole number as needed.)

Let \( d \) be the distance from the building when the angle of elevation is \( 23^{\circ} \). Then the building’s height \( x \) can be written as \[ x = d \tan(23^{\circ}). \] After advancing \( 155 \) feet toward the building, the new distance is \( d - 155 \) and the angle of elevation is now \( 46^{\circ} \), so \[ x = (d - 155) \tan(46^{\circ}). \] Since both expressions represent the height \( x \), we can equate them: \[ d \tan(23^{\circ}) = (d - 155) \tan(46^{\circ}). \] Solve for \( d \): 1. Distribute on the right side: \[ d \tan(23^{\circ}) = d \tan(46^{\circ}) - 155 \tan(46^{\circ}). \] 2. Rearrange terms to isolate \( d \): \[ d \tan(46^{\circ}) - d \tan(23^{\circ}) = 155 \tan(46^{\circ}), \] \[ d \Bigl(\tan(46^{\circ}) - \tan(23^{\circ})\Bigr) = 155 \tan(46^{\circ}). \] 3. Solve for \( d \): \[ d = \frac{155 \tan(46^{\circ})}{\tan(46^{\circ}) - \tan(23^{\circ})}. \] Now, substitute \( d \) back into the expression for \( x \): \[ x = d \tan(23^{\circ}) = \frac{155 \tan(46^{\circ}) \tan(23^{\circ})}{\tan(46^{\circ}) - \tan(23^{\circ})}. \] Using approximate values: \[ \tan(23^{\circ}) \approx 0.4245,\quad \tan(46^{\circ}) \approx 1.0355, \] we have \[ x \approx \frac{155 \times 1.0355 \times 0.4245}{1.0355 - 0.4245}. \] Compute the numerator: \[ 155 \times 1.0355 \times 0.4245 \approx 68.17, \] and the denominator: \[ 1.0355 - 0.4245 \approx 0.6110. \] Thus, \[ x \approx \frac{68.17}{0.6110} \approx 111.47. \] Rounding to the nearest whole number, the height of the building is approximately \[ 111 \text{ feet}. \]