thommagma

% the purpose of this is to determine if Thom can dig a straight line to me
% without burning up inside the mantle. Goodluck Thom.
r = 6378.1 % kilometers , radius of earth
% thickness of the crust ranges between about 20 and 120 km.
s = 5024.000 % km , arc_length

theta = s / r % radians

% isosceles triangle, earth_r, earth_r, secant_line
phi = (pi-theta)/2

% x: r*cos(theta)+x*cos(phi) = r
% y: r*sin(theta)-x*sin(phi) = 0
% where x is 3rd leg in isosceles triangle

x1 = r*(1-cos(theta))/cos(phi) % irrelevant calculations
x2 = r*sin(theta)/sin(phi) % irrelevant calculations

% octave-3.2.3:12> x1 = r*(1-cos(theta))/cos(phi)
% x1 =  4895.1
% octave-3.2.3:13> x2 = r*sin(theta)/sin(phi)
% x2 =  4895.1

% right triangle consisting h=r, leg = x/2 & height(ultimate goal), angles phi(adjacent to x/2) & theta/2
% sin(phi) = height/r
height = r*sin(phi)

% octave-3.2.3:14> height = r*sin(phi)
% height =  5889.8

% with r & height, your maximum depth would be:
max_dep = r - height

% max_dep =  488.31

% you have definitely achieved magma  :S