The grade of a bridge is about $8.24 \%$. Part: 0 / 2 Part 1 of 2 How far does the bridge go up vertically over a span of 1051.8 feet? The height change is about feet.

Step 1 ：The grade of a bridge is the ratio of the vertical rise to the horizontal run. In this case, the grade is given as \(8.24 \%\). This means that for every 100 feet horizontally, the bridge rises 8.24 feet vertically.

Step 2 ：To find out how far the bridge goes up vertically over a span of 1051.8 feet, we need to multiply the horizontal distance by the grade.

Step 3 ：Let's denote the horizontal distance as \(d_h\) and the grade as \(g\). So, \(d_h = 1051.8\) feet and \(g = 0.0824\).

Step 4 ：The vertical distance \(d_v\) can be calculated as \(d_v = d_h \times g\).

Step 5 ：Substituting the given values, we get \(d_v = 1051.8 \times 0.0824 = 86.66832\) feet.

Step 6 ：Rounding to two decimal places, we get \(d_v = 86.67\) feet.

Step 7 ：Final Answer: The bridge goes up vertically about \(\boxed{86.67}\) feet over a span of 1051.8 feet.