Why of all verbs is it 'see'?

Where the picture shows up in てみる

1. 1

   try it on and see

   この服、着てみてもいいですか。

   kono fuku, kite mite mo ii desu ka

   May I try this on?

   Here みる is written in hiragana, not as the kanji 見る.

2. 2

   go on, give it a try

   一度食べてみてください。

   ichido tabete mite kudasai

   Please try it once.

3. 3

   ask and see

   部長に聞いてみます。

   buchō ni kiite mimasu

   I'll ask the manager about it.

4. 4

   want to try it myself

   自分でやってみたい。

   jibun de yatte mitai

   I want to try doing it myself.

5. 5

   tried it, and here's what happened

   電話してみたけど、出なかった。

   denwa shite mita kedo, denakatta

   I tried calling, but nobody picked up.