Possible to get permits for building room near Pine Tree?

I wanted to add 400 sq ft total for a master bedroom and bathroom in the open space of my L shaped house. There is a 40 feet tall 40 feet wide pine tree 6 ft from the corner of this planned new construction. Will the city (Milpitas) give me permits to build?

Cut the tree down

Yes, Joe’s Weekend Tree Trimming service is the best…(don’t Yelp it…)