our teacher entered the

这是一个独立主格结构,有介词in的话,不需要介词with,也不需要物主代词.
如果改成非独立结构,加上介词with,同时也要加上物主代词,变为：with a book in his hand.
下面有详解,你有时间就看看吧：
独立主格结构
非及物动词就是cry,smile,sleep简单说就是这类你一个人就可以完成的动作,所以没有必要用被动语态.你说"我哭了",总不能转变成"我被哭了"吧?
第一个问题说来话长,不知道下面这些材料能不能帮到你~
独立主格结构本身不是句子,在句子中作状语,表示时间、原因、条件、伴随等.常见的独立主格结构有如下几种：
1.名词/主格代词+现在分词.名词/主格代词与现在分词之间主谓关系.如：
The girl staring at him (= As the girl stared at him),he didn”t know what to say.姑娘两眼望着他,他不知道说什么好.
Time permitting (= If time permits),we will go for an outing tomorrow.如果时间允许的话,我们明天去郊游.
2.名词/主格代词+过去分词.名词/主格代词与过去分词之间的动宾关系.如：
The problems solved (= As the problems were solved),the quality has been improved.随着问题的解决,质量已经提高了.
Her glasses broken (= Because her glasses were broken),she couldn”t see the words on the blackboard.由于眼镜摔坏了,她看不见黑板上的字.
3.名词/主格代词+不定式.名词/主格代词与不定式之间是主谓关系,且强调的是一次具体性的动作.如：
He is going to make a model plane,some old parts to help.借助于一些旧零件,他要做一个飞机模型.
They said good-bye to each other,one to go home,the other to go to the bookstore.他们道别后,一个回了家,一个去了书店.
4.名词/主格代词+形容词.如：
An air accident happened to the plane,nobody alive.那架飞机遭遇了空难,无一人生还.
So many people absent,the meeting had to be called off.这么多人缺席,会议不得不取消.
5.名词/主格代词+副词.如：
He put on his sweater wrong side out.他把毛衣穿反了.
The meeting over,they all went home.会议一结束,他们就都回家了.
6.名词/主格代词+介词短语.如：
The boy goes to the classroom,book in hand.那男孩手里拿着书去教室.
Mary was sitting near the fire,her back towards the door.玛丽靠近火炉坐着,背对着门.

our teacher entered the room,with a book in his hand.

hand 先有in , 但是我觉得book 前有个with

这是省略结构 （with a) book in (her/his)hand

老师进到房间，手里拿本书。是不用填冠词啊。