Thread: Another Word Problem.

A surveyor is measuring the distance across a small lake. He has set up his transit on one side of the lake 150 feet from a piling that is directly across from a pier on the other side of the lake. From his transit, the angle between the piling and the pier is 70degrees. What is he distance between the piling and te pier to the nearest foot?

can someone help me with a visual or diagram? the word problem is very confusing and i don't understand how to set up the diagram of the lake, the piling and the pier. what is a piling anyways? thanks!

Originally Posted by CONFUSED_ONE

A surveyor is measuring the distance across a small lake. He has set up his transit on one side of the lake 150 feet from a piling that is directly across from a pier on the other side of the lake. From his transit, the angle between the piling and the pier is 70degrees. What is he distance between the piling and te pier to the nearest foot?

can someone help me with a visual or diagram? the word problem is very confusing and i don't understand how to set up the diagram of the lake, the piling and the pier. what is a piling anyways? thanks!

Per the wordings of your question, there are many possible locations/positions of the piling, pier and transit. But more than likely, the transit to piling is perpendicular to the imaginary line connecting the piling and the pier across the lake. Because if that is not the case, then you cannot solve for the distance between the piling and the pier. You are going to use a triangle to solve for that distance. There are only two numerical data given, 150ft and 70deg, and you need at least 3. That is why the triangle must be a right triangle. That gives another numerical data---one of the angles is 90deg.

A piling is a pile (wooden, or concrete, or steel, or...) driven into the ground, with a portion still sticking out or not fully driven. In that lake, the piling could be for mooring or tying vessels.

Let x = distance between piling and pier.
tan(70deg) = x/150
x = 150*tan(70deg) = 412 ft. -------answer.

Thank you very much ticbol!!!!!!!