Math problem?
I want to bend a piece of steel that is 30' long. The radius is 190'. What will the distance be between a straight line and the center of the bent angle? How do I calculate that if I can't do it physically with a 190' tape measure. If I know the center, then I can do it every 10', 5' or where I need to.
Update:No large parking lot and no long tape measure. My tape measure is only 30' long.
Update 3:The straight line is from one end of the 30' angle to the other end.
Comments
Consider the triangle with one vertex at the center and two vertexes on the ends of the bent steel, one at each end. This is an isosceles triangle with an angle in radians equal to 3/19 (remember that the degree in radians is simply the length of the arc subtended by the angle divided by the length of the radius). Now consider the altitude from the center to the short side of the triangle. Clearly, this line will bisect the angle and divide the triangle into two equal right triangles, both having a hypotenuse equal in length to the radius and an angle of one half the small angle in the isosceles triangle (3/38). The altitude itself is the side adjacent to this angle and also the distance between the center and the midpoint of the straight line between the two ends of the bent steel. The distance between the midpoint of the bent steel, and the midpoint of this line, is equal to the radius minus the length of the altitude. Since the cosine of an angle is equal to the length of the adjacent side is equal to the proportion of the adjacent side to the hypotenuse (which in this case is the altitude and the radius, respectively), it follows that the length of the altitude is equal to the radius times the cosine of 3/38. Thus the distance you are looking for is:
190 ft - 190 ft * cos(3/38)
190(1-cos(3/38)) ft
approx. 7.1 in
You can't bend a piece of steel whose diameter (380') is longer than its width (30'). What could you do with an absurdly wide and short piece of steel like that anyway?
Lindasue, the radius is shorter than the length. Are train tracks like that? No, they aren't.
Don't listen to the nay-sayers. Yes, you can. Just imagine a train track, they bend them to whatever arc they need. I would suggest you use a big parking lot, a long tape measure and some sidewalk chalk. A piece of yellow nylon string might help. You can do it !
the distance is 120
Two words:Scale model
I can't answer your question, your facts are uncoordinated and non sequitor
you can't bend steteel that is that long and that wide
I have to ask; WHY?