Most entryway hooks were put up by whoever built the house or whoever moved in first, and they were set at a height that felt right to that person. Your father reaches for his coat every day, and he has his own way of doing it: one hand on the hook, the other steadying the collar, a little tug. A hook set in the wrong place makes that routine harder than it needs to be, and in winter, when the coat is heavy and the boots are wet, it adds up. The job is to measure for him, not for a catalog.
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Measure his reach
Have him stand in his usual spot by the door, wearing his regular indoor shoes, with his arm relaxed at his side. Ask him to reach up as if he were taking a coat off a hook. Mark the spot where his hand comfortably closes, and mark the spot where he would have to lift his shoulder to get there. The top hook should sit below that second mark, so he never has to raise his shoulder past a comfortable line to take a coat down. The lowest hook should be at a height where he can hang a coat without bending far. You are looking for a range he can use without thinking about it.
If he wants to do the measuring himself, let him. A man who sets his own hooks will use them. If he would rather you measure, ask him to stand still while you do it and do not argue about the marks.
Space the hooks for the winter coat
A light jacket can share a hook with a neighbor. A heavy winter coat cannot. Look at the coat he actually wears in January, not the one in the closet from a milder season. Lay it over the hook and see how far the sleeves and collar fall. Leave enough room that the coat hangs without bunching, and that the hook next to it is not covered. Two or three wide-set hooks often serve a household better than five crowded ones. Add one hook for a bag or a hat, set above the coat hooks where it will not drag the coats down.
Check the clearance
Open the front door fully and watch where it swings. The hooks must sit outside the arc of the door, or the door will catch a coat when it opens and throw it to the floor. Also check the wall behind the hooks. Mount them into the wall framing, not just into the drywall, because a full winter coat with a wet hat in its pocket pulls harder than most people expect. A stud finder is worth borrowing if you do not own one. If the wall is plaster or brick, use the anchor the hardware store recommends for that material, and read the package before you buy.
What to do tonight
Take the coat he wears most and hang it on the hook you think is right. Have him take it down and put it back on. If the sleeve catches or the coat drops to the floor, move the hook. Mark the new spot with a pencil. If the spot works, you can mount the hooks tomorrow. Tonight, just check that the coat comes down without a struggle, because that is the test that matters.
Keep her coat in mind
There may be a coat of your mother's still hanging in the closet or on the rack. You do not need to move it tonight. If you decide to keep it out, give it its own hook in a spot that does not get in his way, and leave it there until you are ready. The end of the row, near the wall, works well for a hook outside the daily route, because it can hang without anyone reaching past it.
When to ask the doctor
If his grip or his balance changes, or if he needs to lean on the wall to get a coat on, bring it up with his doctor at the next visit. A hook at the right height helps, but it does not replace a conversation about what is changing. If he is hiding how hard it has become to get dressed, you will often notice it first in the entryway, so keep an eye on the coat.