Question

During the summer​ heat, ​8 mi bridge expands 8 ft in length. Assuming the bulge occurs straight up the​ middle, how high is the​ bulge?

Answer 1

we shall consider length of half bridge.
expansion is also half and=4 ft
half the bridge=1/2*8=4 mile=4*1760*3=21120 ft
original length=21120 ft
length after expansion=21120+4=21124 ft
to find the height we use pythagoras theorem
\[h=\sqrt {21124^2-21120^2}=\sqrt{(21124+21120)(21124-21120)}\]
\[=\sqrt{42244*4}\]
\[=\sqrt{10561*4*4}\]
\[=4\sqrt{10561}\]
\[\approx 411.07 ~ft\]
\[\approx 137 yards.\]