doseogwaneseo gongbuhadaga chinguege yeonrakhaesseoyo.

-다가 links two actions and usually means:

• while doing X
• then Y happened
• often with a feeling that the first action was interrupted or paused

So 도서관에서 공부하다가 친구에게 연락했어요 suggests:

• I was studying at the library,
• and then I contacted my friend.

This is a little different from -고, which is often just a simple and/then connection.

Because 에서 marks the place where an action happens.

Here, 공부하다 is an action, so the location takes 에서:

• 도서관에서 공부했어요 = I studied at the library.

By contrast, 에 is commonly used for:

• destination: 도서관에 갔어요 = I went to the library
• existence/location with 있다/없다: 도서관에 있어요 = I am in the library

So in this sentence, 에서 is the correct particle.

You take the verb stem and add -다가:

• dictionary form: 공부하다
• stem: 공부하-
• • 다가
• result: 공부하다가

So although it looks like 공부하다 + 가, grammatically it is:

• 공부하- + 다가

This same pattern works with many verbs:

• 먹다 → 먹다가
• 가다 → 가다가
• 전화하다 → 전화하다가

에게 marks the person receiving the action.

With 연락하다, the person being contacted is marked with 에게 (or 한테 in casual speech).

So:

• 친구에게 연락했어요 = I contacted my friend
• more literally: I made contact to my friend

It works a lot like English to in this kind of sentence.

Yes. 친구한테 연락했어요 is very natural.

The difference is mostly style:

• 에게 = neutral, slightly more formal, common in writing too
• 한테 = more conversational
• 께 = honorific, used for someone you should show respect to

Examples:

• 친구한테 연락했어요 = casual/natural
• 친구에게 연락했어요 = neutral
• 선생님께 연락했어요 = respectful

This is the past polite form.

The steps are:

• 연락하다
• stem: 연락하-
• add past polite ending: -았/었어요
• 하다 verbs become 했어요

So:

• 연락하다 → 연락했어요

This comes from a contraction of 하였어요, which becomes 했어요.

The same thing happens in many 하다 verbs:

• 공부하다 → 공부했어요
• 일하다 → 일했어요
• 운동하다 → 운동했어요

Yes. Korean often leaves out the subject when it is already understood from context.

So this sentence could mean:

• I contacted my friend
• he/she contacted a friend
• we contacted a friend

In a textbook example, it is often translated as I contacted my friend, but the Korean sentence itself does not explicitly say I.

In Korean, when a verb appears in a connecting form like -다가, it often does not show tense directly. The tense is usually understood from the final verb.

Here, the final verb is 연락했어요, which is past tense, so the whole sentence is understood as past:

• I was studying at the library,
• then I contacted my friend.

So even though 공부하다가 does not contain an obvious past marker, the sentence still refers to past events.

Usually it suggests that the first action was in progress, and then the second action happened, often with a sense of switching or interrupting.

So here the natural feeling is:

• I was studying,
• then I paused or stopped that activity to contact my friend.

It does not always mean a complete permanent stop, but it often implies a break in the first action.

That is one reason this sentence feels different from:

• 도서관에서 공부하고 친구에게 연락했어요

That version is more like a simple sequence: I studied at the library and then contacted my friend.

The difference is mainly nuance.

• 공부하다가 친구에게 연락했어요

  • I was studying, and then I contacted my friend.
  • suggests an interruption or change during the first action

• 공부하고 친구에게 연락했어요

  • I studied and then contacted my friend.
  • more neutral sequence, less emphasis on interruption

So -다가 is a better choice when the speaker wants to show that the second action happened during the first activity or caused a shift from it.

Most naturally, 도서관에서 goes with 공부하다가:

• 도서관에서 공부하다가 = while studying at the library

So the structure is:

• 도서관에서 = at the library
• 공부하다가 = while studying / while I was studying
• 친구에게 연락했어요 = I contacted my friend

In context, listeners may also naturally assume the contact happened there too, but grammatically 도서관에서 most directly describes the studying part.