Isn't "who"/"whose" only used for people?

Why is the usage of whose correct in the following sentence:

In the foothills of that large mountain range are the sources of a river whose course was not fully mapped until this century.

I was under the impression that you have to use which or that when referring to things. When is it okay to use who/whose to modify things?

I thought the sentence would have to be something like "...are the sources of a river, the course of which was not fully mapped..."

Solution 1:

You can use 'whose' but not 'who' with things.

'Which' does not have a possessive. You cannot say 'the house which's chimneys are red'; for 'which's' doesn't exist. Somebody like John Lawler or Edwin Ashworth may be able to explain why.

It is perfectly alright to use 'whose' in the context in which you have shown it. My assumption that the reason for that is that 'which's' is not available.

You cannot use 'who' in the nominative or accusative case with things. You could not, for example say 'Who is the river you are discussing'. It would have to be 'Which is the river you are discussing'. Nor could you say 'The house, the chimneys of who are red'. You would have to say 'The house, the chimneys of which are red'.

But in the genitive, 'The river whose waters are muddied' is perfectly alright, for some reason which I do not fully understand. No doubt there is an interesting history to this.

Solution 2:

The use of whose is not limited to people.

Mr. Waits said he had heard Mr. Kaczynski cursing the dogs, whose barking may have betrayed his location in the woods. - the New York Times Whose is not limited to people.

The cab drew up at the house whose windows were lit up. - Virginia Wolfe

The sun whose light we sail upon: A blazing summer dandelion.

...an appreciable advantage in observing the moon, whose light is simply reflected... - Jules Verne

The mountain, whose peak rises around 2700 feet above average Martian surface level... - science.kqed.org

... the modern-day story of how the Library of Congress came to find---and then authenticate---the rare untrimmed version of the book whose pages you will see.