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The circular arc of a railroad curve has a chord of length 2500 feet corresponding to a central angle of 35". Find the length s of the circular arc. If needed,

The circular arc of a railroad curve has a chord of length 2500 feet corresponding to a central angle of 35".
Find the length s of the circular arc. If needed, use 3.14 for π. Round to the nearest whole angle.
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1 Answer

So Coco,
1) Have you drawn a diagram for this problem yet? If not, you should do that first, because it will give you an idea of what to do next.
2) Now that you've drawn a diagram, you see that you have an isosceles triangle defined, with the third side length 2500 ft., and the central angle of 35" -- it it really " = seconds?? I think you meant o , degrees, right? I'll assume you meant degrees, which would be reasonable; (if you really meant seconds, then you'll solve in the same general way, the radius of the circle is going to be enormous however).
3) So you have a pair of matched right triangles then defined (each taking half the isosceles area), each with an angle 35/2 degrees opposite a side of 2500/2 ft.
4) Solve by trig for the hypotenuse length: sin (35/2)= 1250 ft./h
5) Use h and the original central angle (35o) to determine the arc length s (proportion to the entire circle C=2πr, where r = h you just found, and the 35o is a proportion of 360o = 2π)
6) Check your answer for reasonableness: it should be slightly more than 2500 ft.
7) If that angle really was 35 seconds, the arc will be almost flat, so of length only a tiny bit more than 2500 ft.
Hope this walk-through helped you.
-- Stanton D. 

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