Case determination (German)
Translate: I have played tennis with Angela in the park yesterday.
Ich habe gestern mit Angela im Park Tennis gespielt.

Should I write "im park" or "in park"? The grammar book says "im park" but isn't "im" the short form of "in dem", meaning that this is the dative case? Why is this the dative case? Is it because the "mit" in "mit Angela" before hand makes it dative?

Question

Case determination (German)
Translate: I have played tennis with Angela in the park yesterday.
>>Ich habe gestern mit Angela im Park Tennis gespielt.

Should I write "im park" or "in park"? The grammar book says "im park" but isn't "im" the short form of "in dem", meaning that this is the dative case? Why is this the dative case? Is it because the "mit" in "mit Angela" before hand makes it dative?

Answer

"In" is a "Wechselpräposition" that can have either dative or accusative case. As Alla said already, dative is used to refer to a location (wo?), while accusative is used for a direction (wohin?). Therefore it's "ich gehe IN DEN Park", but "ich spiele IM Park". The "mit Angela" has nothing to do with it.

http://www.mein-deutschbuch.de/lernen.php?menu_id=84
https://coerll.utexas.edu/gg/gr/cas_09.html

Answer

I try to explain with my basic English.

Yes. "Im Park" it means "in dem Park". And it is dative case. The same is "mit Angela" is it dative too. 
Dative answers the questions "(with) whom" and "where / where from".  In German "wem, wo, woher".

1. Mit wem habe ich Tennis gespielt? Mit Angela.
2. Wo habe ich Tennis gespielt? Im Park.

You must to set apart from the Akkusativ. This answers the questions "wen/was" and "WOHIN".

Answers · 4

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