Oscillating path

It's the same as asking the length of a straight path at $10$ degrees to reach an altitude of $15$ , so $15Csc(10) = 86.3816$

The half-angle at the apex is given by arctan(5/15) = 18.43494882, giving the lower left angle = 71.56505118, and the lowest triangle has the other 2 angles = 10 and 98.43494882.. if the first slant line is d 1, by the law of sines we have (d 1)/sin(71.56505118) = 10/sin(98.43494882), so d 1 = 9.59057381. We can easily work our way up the triangle, and from the law of sines, we find d n+1 = (d n)sin(61.56505118)/sin(98.43494882) = .888974289*(d n). This leads to the geometric progression: (d 1)*(1 = r + r^2 + r^3 +...……) with r = .888974289. The sum = (d 1)*[1/(1 -r) = 86.382. Ed Gray