Angles of Elevation and Depression

[bookworm396]

I'm having trouble with the problem below:

State an equation that would enable you to solve each problem. Then solve. Round answers to the nearest tenth.

27. The waterway between Lake Huron and Lake Superior separates the United States and Canada at Sault Sainte Marie. The railroad drawbridge located at Sault Sainte Marie is normally 13 feet above the water when it is closed. Each section of this drawbridge is 210 feet long. Suppose the angle of elevation of each section is 70 degrees. Find the width of the gap created by the two sections of the bridge.

I attempted to use the equation Cosine 210=90/x to solve, but this did not work. I also tried to use equations Tangent and Sine to solve the problem, but didn't come up with a reasonable answer. If anyone could help, it would be greatly appreciated.

 

[Deleted member 4993]

I'm having trouble with the problem below:

State an equation that would enable you to solve each problem. Then solve. Round answers to the nearest tenth.

27. The waterway between Lake Huron and Lake Superior separates the United States and Canada at Sault Sainte Marie. The railroad drawbridge located at Sault Sainte Marie is normally 13 feet above the water when it is closed. Each section of this drawbridge is 210 feet long. Suppose the angle of elevation of each section is 70 degrees. Find the width of the gap created by the two sections of the bridge.

I attempted to use the equation Cosine 210=90/x to solve, but this did not work. I also tried to use equations Tangent and Sine to solve the problem, but didn't come up with a reasonable answer. If anyone could help, it would be greatly appreciated.

First sketch the situation:

A          B    C         D
  |        /     \        |
  |      /         \      |
  |    /             \    |
  |  /                 \  |
E |_______________________| F

BE = CF = 1/2 * 210

AB = CD = BE * cos(70°)

The gap = BC = AD - 2*AB

Now finish it....