i have some issues with this. Could anyone explain me if it is right /wrong
? that is the link/image of my work
-You are lying on a beach, your eyes 20 cm above the sand. Just as the Sun sets, fully disappearing over the horizon, you immediately jump up, your eyes now 150 cm above the sand, and you can again just see the top of the Sun. If you count the number of seconds until the Sun fully disappears again, you can estimate the Earth’s radius. But for this Problem, use the known radius of the Earth to calculate the time t.
Thanks in advance
Your calculation of $x,\,y$ is correct but overly complicated as they're in right-angled triangles, so you don't need the cosine rule. (Since both cosines are very close to $1$, we also have the approximations $x\approx\sqrt{40/R}$ etc. in radians.) You're also right that each degree takes $4$ minutes to traverse.
But your result contains a spurious factor of $2$. You seem to think the Sun only disappears when angles of $2x$ or $2y$ have been subtended, rather than when angles of $x$ or $y$ have been subtended, taking us to the point where the line of vision is tangential to Earth's surface.