Why does a mountaineer feel the blood in the nose at too much height?

Why does a mountaineer feel the blood in the nose at too much height?

At too much height, blood pressure is greater than atmospheric pressure,
that’s why a mountaineer feels blood in his nose. Air density and pressure are
reduced as one goes up from the earth’s surface. At the higher point, the
atmospheric pressure becomes so much low, that blood pressure becomes greater
than this.

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