Question

I have a math question. How would I set this up?:
During the summer heat, a 10 mile bridge expands 10 feet in length. Assuming the bulge occurs straight up the middle, how high is the bulge? Answer in feet by unsimplified radicals first, then simplify the radical and round to the nearest thousandth.

Answer 1

This is intended to be a trigonometry problem, I think. Imagine the bridge in half-spans, each one 5 miles. At start the half-span is "horizontal". Then it becomes 5 miles + 10 feet, but now it is tilted up, being the hypotenuse of a triangle. The distance from land to middle of bridge is still 5 miles, horizontal. So you have a triangle with base 5 miles, hypotenuse 5 miles + 10 feet. Can get the cosine of angle from that. Then calculate the sine, and figure out how long the vertical side in middle is approx.

Good luck!

Answer 2

easier method:
Pythagoras Theorem: a^2 + b^2 = c^2

with:
a:= bulge height
b:= half of the bridge = 5miles
c:= slope = (10miles + 10feet)/2

so:
a^2 + b^2 = c^2
a^2 = c^2 - b^2
a = sqrt(c^2 - b^2)
a = sqrt( ((10ml+10ft)/2)^2 - (5ml)^2 )

Answer 3

Thank you VERY much to both of you!!!