Differentials Problem

Question

a ship is 1/2 mile from the base of a bridge. The angle of elevation from the boat to the top of the bridge is 3 degrees with a possible error of plus or minus 0.15 degrees. what is the calculated height of the bridge. Use differentials to determine the maximum error in the height of the bridge. if the ship stands 135 feet out of the water should the captain continue and attempt to pass under the bridge? Explain your answer.

Answer 1

There are three triangles to consider. The most important triangle is the shallowest one which we may call the low margin triangle. This triangle has a measure of 2.85 degrees.

 

We have A=2.85 and side equal to .5.

 

We use tan(2.85) = x/.5 .

 

we get  .024 miles which is 127 feet. Unfortunately that is too small for the ship and it should not continue.