A curve on a light rail track is an arc of a circle of length 300m and the straight line joining the two ends of the curve is 270m long.
a) show that, if the arc subtends an angle of 2x(degrees) at the center of the circle, x is a solution of the equations
sin x(degrees) = (pi*x)/200
b) solve, correct to 2 d.p., the equation for x
Name:
Anonymous2008-12-13 15:11
Too lazy to do pictures
a) Because things should always be in radians unless you're in third fucking grade, rewrite the equation as
sin x = 9/10 x
where x is in radians
The triangle defined by the given chord and the center of the circle splits into two right triangles with sides R sin x, R cos x, R. We are given R sin x = 135. But also the length of the arc is 2xR = 300 or xR = 150. Eliminate R and the formula you want drops out.