So let's get it started.

讓我們開始吧。

It's loading up.

正在加載

All right make sure you can see our screen.

好了，確保你能看到我們的螢幕。

Actually in this form...

實際上，在這種形式下...

Hello there.

你們好

I'm here with my son and I'd love you to tutor him on this math problem but don't give him the answer.

我和我兒子在一起，我希望你能輔導他這道數學題，但不要告訴他答案。

You can ask questions and nudge him in the right direction but I really want to make sure he understands it himself and he's here in the room so you can talk to him directly.

你可以提出問題，引導他朝著正確的方向前進，但我真的想確保他自己能理解，而且他就在房間裡，你可以直接和他交流。

Of course I'd be happy to help.

我當然樂意幫忙。

Let's look at the problem together.

讓我們一起來看看這個問題。

Can you first identify which sides of the triangle are the opposite adjacent and hypotenuse relative to angle alpha?

你能首先確定三角形中相對於角 alpha 的對邊和斜邊是哪幾條邊嗎？

All right so I'm pretty sure this is the angle alpha right here, right?

好吧，我很確定這裡就是阿爾法角，對嗎？

Correct.

正確。

Now looking at the triangle which side do you think is the hypotenuse?

現在看看這個三角形，你認為哪一邊是斜邊？

Remember the hypotenuse?

還記得斜邊嗎？

I'm not totally sure.

我不太確定。

I think it might be this one but I really am not sure.

我想可能是這個，但我真的不確定。

This side AC?

這邊是空調？

You're close.

就差一點了

Actually side AC is called the adjacent side to the angle alpha.

實際上，邊 AC 被稱為角 alpha 的鄰邊。

The hypotenuse is the longest side of a right triangle and is directly opposite the right angle.

斜邊是直角三角形的最長邊，與直角直接相對。

Can you find which one is the hypotenuse?

你能找出哪個是斜邊嗎？

Oh okay I see.

哦，好吧，我明白了。

So I think the hypotenuse is this really long side from A to B.

所以我認為斜邊就是從 A 到 B 的這條很長的邊。

Would that be correct?

這樣做對嗎？

Exactly.

沒錯。

Well done.

幹得好

Now that you've identified the hypotenuse can you identify which side is the opposite side to angle alpha?

既然你已經確定了斜邊，那麼你能確定哪一邊是角α的對邊嗎？

Okay well I mean you told me earlier that this was the adjacent side and I know that's the hypotenuse so I'm guessing that this side BC is the opposite side.

好吧，我是說你之前告訴我這是鄰邊，我知道那是斜邊，所以我猜 BC 這一邊是對邊。

Great deduction.

扣得好。

That's absolutely correct.

完全正確。

Now that you've identified all the sides relative to angle alpha do you remember the formula for finding the sine of an angle in a right triangle?

現在你已經確定了所有與角 alpha 有關的邊，還記得求直角三角形中一個角的正弦值的公式嗎？

Yeah I know that the sine is equal to the opposite over the hypotenuse.

我知道正弦等於斜邊上的反弦。

Perfect that's absolutely right.

很好，完全正確。

Now can you apply that formula to find sine alpha in the triangle using the lengths of the sides that we've identified?

現在，你能應用該公式，利用我們確定的邊長求出三角形中的正弦α嗎？

Okay so I mean you told me that 7 this side BC is the opposite side and then you said that the hypotenuse is longest side so that would be this side AB which is 25.

好吧，我是說你告訴我 BC 這一邊是對邊 7，然後你又說斜邊是最長的一邊，所以就是 AB 這一邊，也就是 25。

So would the answer be 7 over 25?

那麼答案會是 7 比 25 嗎？

Excellent work.

幹得漂亮

That's correct.

沒錯。

Sine alpha equals 7 over 25.

正弦α等於 7 乘以 25。

You did a great job identifying the sides and using the sine formula.

你在確定邊線和使用正弦公式方面做得很好。

If you have any more questions feel free to ask.

如果您還有任何問題，請隨時提出。