A 60m long bridge has an opening in the middle and both sides open up to let boats pass underneath. The two parts of the bridge floor rise up to a height of 18 m. Through what angle do they move?
Draw a diagram. You will see that
sinθ = 18/30
Extra credit: How wide a ship can pass through the opening?
To find the angle through which the bridge floor moves, we can use trigonometry. Let's assume that the two halves of the bridge floor move up symmetrically, forming a right triangle with the base being the distance from the center of the bridge to one side, and the height being the vertical displacement of the bridge floor.
We have a right triangle with a base of half the length of the bridge (60m/2 = 30m) and a height of 18m. We want to find the angle θ, which is the angle opposite to the height side.
Using the tangent function, we can calculate the angle:
tan(θ) = (height / base) = 18 / 30
To find θ, we can take the inverse tangent of both sides:
θ = atan(18 / 30)
Using a calculator, the inverse tangent of 18/30 is approximately 29.4 degrees.
Therefore, the bridge floor moves through an angle of approximately 29.4 degrees.