sono sensyu no gooru wo mite, kazoku mo ookina koe de ouensita.

その means that and points to a specific player that is already known in the context.

So その選手 means that player.

Japanese has three common demonstratives of this type:

• この = this ... (near the speaker)
• その = that ... (near the listener, or already mentioned)
• あの = that ... over there / that one we both know

Here, その tells you this is not just any player, but a particular player already being talked about.

Here の shows a relationship between two nouns. In this sentence, it means something like:

• the player’s goal
• the goal by that player

So その選手のゴール means that player’s goal.

This is a very common use of の:

• 私の本 = my book
• 日本の文化 = Japanese culture
• 田中さんの車 = Tanaka’s car

In sports, Xのゴール is very natural for X’s goal.

Because ゴール is the direct object of 見る.

• 見る = to see/watch
• ゴールを見る = to see the goal

So を marks the thing that was seen.

Even though ゴール is a noun borrowed from English, it behaves like a normal Japanese noun and can take particles the usual way.

見て is the て-form of 見る.

In this sentence, it connects 見る to the next action:

• ゴールを見て、家族も応援した
• Seeing the goal, the family also cheered
• After seeing the goal, the family also cheered

The て-form often links actions like this. Depending on context, it can feel like:

• and
• when
• after
• upon

Here it suggests that seeing the goal led into the cheering.

It can suggest more than one of those at once.

In this sentence, 見て most naturally gives a sense of:

• when/after seeing
• and possibly a mild sense of because they saw it

So the idea is that the family saw the goal, and that prompted them to cheer.

This kind of slight overlap is very common with the て-form. Japanese often leaves the exact relationship a little flexible, and English has to choose a clearer wording.

も means also or too.

So 家族も means the family also or the family too.

It implies that someone else was also cheering, or that the family joined in as well.

Also, も often replaces は or が rather than appearing alongside them. So instead of saying:

• 家族が = the family
• 家族は = as for the family

the sentence uses:

• 家族も = the family too

That is why you do not see 家族がも or 家族はも.

Most likely, yes: it will usually be understood as the player’s family from context.

However, the sentence itself only says 家族. It does not explicitly say:

• その選手の家族 = that player’s family

So grammatically, 家族 just means the family, and the listener uses context to decide whose family it is.

Japanese often leaves things unstated when they are easy to infer.

The sentence does not say explicitly, because Japanese often omits things that are obvious from context.

So 応援した here means something like:

• cheered
• cheered them on
• supported them

The most natural understanding is that the family cheered for:

• that player
• or that player’s team

because that is what the surrounding context suggests.

Both 大きな声で and 大きい声で are possible.

But 大きな声 is a very common and natural expression meaning:

• a loud voice
• in a loud voice

A useful point:

• 大きい is the regular -い adjective
• 大きな is a special form used only directly before a noun

So you can say:

• 大きい = big
• 大きい声 = a loud/big voice
• 大きな声 = a loud voice

In this phrase, 大きな声 is especially common and natural.

Here で marks the manner or means of the action.

So:

• 大きな声で応援した = cheered in a loud voice
• or cheered loudly

This is not the で of location. It is the で that tells you how the action was done.

Compare:

• 電車で行く = go by train
• 日本語で話す = speak in Japanese
• 大きな声で言う = say in a loud voice

Same basic idea: by means of / in / with.

応援した is the plain past form of 応援する.

• 応援する = to support / to cheer
• 応援した = supported / cheered

Because it ends in する, this is a suru-verb:

• 応援する
• 応援して
• 応援した

In this sentence, it clearly refers to a past action: the family cheered.

By itself, 応援する can mean either:

• to support
• to cheer on

But in this sentence, 大きな声で makes it clear that it is actual vocal cheering.

So the nuance is not just silent support. It is more like:

• cheering loudly
• shouting encouragement

In sports Japanese, ゴール can refer to the goal/result in a way similar to English.

In this sentence, その選手のゴールを見て most naturally means they saw that player score or saw that player’s goal happen.

So it is less about staring at the physical goalpost or net, and more about witnessing the scoring moment/result.

It breaks down like this:

• その選手のゴールを見て、
  seeing/after seeing that player’s goal

• 家族も
  the family also

• 大きな声で
  in a loud voice

• 応援した。
  cheered

So the structure is:

[Clause 1 in て-form], [main clause].

This is a very common Japanese pattern:

• do A, then do B
• upon doing A, B happened
• A happened, and then B

Here:

• seeing the goal leads into
• the family also cheering loudly