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This is a map of mudflows from a normal type eruption. Enough to endanger a couple hundred thousand people.
A large lateral blast (like St Helens) to the NNW would reach Seattle.
Seattle is about as far from Mount Rainier as Mt. Rainier is from Mount St. Helens, about twice as far as the kill zone from the St. Helens blast (referring to the blast itself). The sideways eruption also seems to be rather rare (in fact, unheard of by geologists prior to St. Helens). The sound of the blast can go quite far (St. Helens' eruptive blast was heard in British Columbia, Canada), but the actual searing shock wave from St. Helens 'only' went about twenty miles (twenty miles is plenty huge for something travelling at the speed of sound killing absolutely everything, of course). If Rainier produced giant mudflows, to the extremes it has in millennia past, it could potentially push a mudflow through 'the Valley' (a valley with no well-known name as it is not a river valley through which State Route 167 goes and includes the cities of Sumner, Auburn and Kent with Renton capping its northernmost extent) to Renton and into Lake Washington, which borders Seattle's eastern edge, but even if that generated flooding and/or tsunami on Lake Washington, Seattle would have relatively minor direct effects aside from the Rainier Beach area as much of Seattle is on a hill between Lake Washington and Puget Sound. The most likely effects Seattle would incur would be ashfall and I-5 getting severed (the major north-south interstate of the West Coast that goes from the Canadian border to the Mexican border, and connects Seattle and Los Angeles) by the bridge over the Cowlitz River getting potentially washed out and/or flooded and choked with debris, as well as Seatac and all other area airports being shut down due to ash in the air. We've had some debilitating isolations a few times in the past when I-5 was closed down due to flooding on the Cowlitz to the south, and I-90 to the east closed due to mudslides or avalanches from the same heavy precipitation that caused the Cowlitz to flood, effectively severing all land transportation routes from the Seattle area. Rainier erupting could do all that plus shut down air travel, plus much of our regional power comes from local hydroelectric dams such as the one on the Puyallup River which could be destroyed by even a moderate lahar on the Puyallup river.
I currently live about 28 miles from Rainier a bit southwest of Orting on that map, as the crow flies, but on an exposed hill, so there would probably be some effect here ... though I'll likely be moving soon to someplace that, sadly, has less of a view but is far more exposed to a lahar along the Puyallup river.