Suppose that p- and s-waves traveled in straight lines through the Earth (in fact, they don’t,…

Suppose that p- and s-waves traveled in straight lines through
the Earth (in fact, they don’t, but we will make this approximation
for this problem). Also suppose that the angular distance from the
epicenter (location of the earthquake) on the Earth’s spherical
surface to the location on the surface beyond which no s-waves can
be observed from an earthquake (the angle between the earthquake
epicenter and the s shadow zone) is 120 degrees (i.e., the two
points are located 1/3 of the Earth’s circumference from each
other). What is the radius of the liquid outer core of the Earth
divided by the radius of the Earth (i.e., what is their ratio)?
Hint: draw a diagram and use trigonometry to find the answer. Do
not give the answer in km or miles, but as a fraction of the
Earth’s radius.