Question 325204: A surveyor is measuring the distance across a small lake. He has set up his transit on on side of the lake 130ft 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 55degrees. What is the distance between the piling, and the pier to the nearest foot?
This question has badly confused me, any help is appreciated. Thanks.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! Surveyor is on one side of the lake.
Set up his transit 130 feet from a piling that is directly across from a pier on the other side of the lake.
The piling is on his side of the lake.
From his transit, the angle between the piling and the pier is 55 degrees.
What is the distance between the piling and the pier to the nearest foot.
From the way this problem is worded, I gather the following:
transit 130 feet piling
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
x x x
x 55 degrees x
x x x
x x
x x
x x
x x
lake between x x
piling and pier x x
x x
x x
x x
x x
x x
x x
x
pier
A right triangle is formed with the 90 degree angle at the piling.
Straight Trigonometry applies to get the other sides.
Side between piling and pier is given by formula:
tan(55) = x / 130
Multiply both sides of this equation by 130 to get:
tan(55) * x = 130
Divide both sides of this equation by tan(55) to get:
x = 130 / tan(55) = 91.02697997 feet which is roughly 91 feet.
That's the distance between the piling and the pier.
The assumption being made here is that the line from the transit to the piling is perpendicular to the line from the piling to the pier.
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