Sorry Skeeter, my mistake 380 miles is correct
The horizon makes a 90 degree angle with the Earth's centre.
This is because the astronaut's line of sight makes a tangent with the planet
(if you balance a perfectly round ball on a table, it's centre is directly above the point of contact or tangency).
The triangle has the same sides and angles,
so the trigonometry works exactly as skeeter originally outlined.