# Find the change in height of a bridge

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1. Apr 29, 2017

### frozen-pizza

1. The problem statement, all variables and given/known data
A bridge with a steel framework is 500.000m long on a winter day at 5.0 C. For steel use 11.0x10^-6/ dC a) Find the length of the bridge on a summer day when the bridge temperature is 55.0 C. Keep 6 significant figures in this part and in part b). The bridge is built in the winter with the two ends anchored in rock and it has a hinge at its center. In the summer at 55.0 C the bridge will be raised as shown below. b) How long is one half of the bridge at 55.0 C? c) Find the distance y that the hinge is above its original position when the bridge is at 55.0o C.

2. Relevant equations
dL=L1*11x10^-6*dC

3. The attempt at a solution
for a i got 500.275 m and for b 250.138, iam having problems with part c
i thought that i could use a 30 30 triangle to find the height but it is not working out

2. Apr 29, 2017

### haruspex

you o not know the angle, so that is not going to work.
Did you draw a diagram? Do you see a right-angled triangle in it?

3. Apr 29, 2017

### frozen-pizza

yea the angle at the line drawn between the hinges right?

4. Apr 29, 2017

### haruspex

That's not very clear. I assume you mean a vertical line through the hinge makes a right angle with the horizontal line between the end supports.
Call the end points A, B, the hinge H, and the point where the right angles are O. So AOB is the line of the bridge in winter.
How far is AO? How far is AH? What relates them to the y=OH?