Why are mountain shadows always triangles?

The 2nd picture unfortunately gives away the answer, so I can't take credit for a brilliantly insightful answer. It's a consequence of perspective, which "sharpens" peaks of mountains, even if their summits aren't necessarily very peak like. Let's say we have a "sloppy summit" mountain, like an asymmetrical pyramid with the top lopped off. It casts a shadow far into the horizon, and perhaps even beyond the horizon where it reduces light backscatter in the air in the distance. The summit irregularity by that time, in the great distance, will look very small to one standing on the summit. Hence, it's as if the silhouette of the mountain has been "pinched" at the top, so that such shadows of all mountains look about the same. You don't see this effect if the shadow is not far away, like, say, across a canyon.

You can make anyone look like a pinhead by same means of stretching the silhouette.

because mountains are cone shaped which in a flat surface world look triangle i wont knock you for asking that question but its too easy lol.

Um...mountains are "triangles"...triangular in frontal shape.

Objects tend to cast shadows of their shape in some regards.

'Cause mountains are conical in shape .