A drawbridge is l = 110 feet long when stretched across a river. As shown in the figure below, the two sections of the bridge can be rotated upward through an angle of α = 34°.

Question

a)If the water level is 35 feet below the closed bridge, find the distance d between the end of a section and the water level when the bridge is fully open. (Round your answer to one decimal place.)
b)Approximately how far apart are the ends of the two sections when the bridge is fully opened, as shown in the figure? (Round your answer to one decimal place.)

Answer 1

Draw a diagram and review your basic trig functions. You will see that the height the section has been raised is

h/55 = sinα

The horizontal distance from the bank is x = 55cosα

So, the end has moved 55(1-cosα) ft closer to the bank.

Now you can answer the questions.