My dad and I were stretching/exercising one morning in our apartment when the sun came up over the mountain on the east side of the city. The room suddenly lit up significantly, and the light from the window was on the wall. Thus, the top of the light on the wall, the top of the window, and the top of the mountain where in line with each other.
“You should be able to figure out how tall that mountain is” said my dad. After breakfast I worked on it, and within 10 minutes had procured an answer. Accounting for the elevation of Santiago, the height of our building, how far away the top of the mountain is (using google maps), and the angle that the point on the wall and the top of the window create (I used right triangles (A run of _ feet results in a gain of _ feet)), and my answer was just under 10,000 feet.
Then my dad noticed — sighting off of our porch rail — that the snow-capped (at the end of summer!) mountains to the northeast were at roughly the same angle up from us as the closer ones directly east. So, I got back on google maps and then re-calculated the angle over the new distance. My answer was 18,600 feet.
Later, I looked up the big mountain (Cerro el Plomo) on wikipedia, and It’s official height is 17,800 feet.
Here is the smaller, closer, 10000 footer.