Pronumeral stuff

[hard timber]

I’ve got an exam tommorow and I am super confused on this question. Please help😭

[glad tiger]

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[willow pecan]

Try finding side x using angle θ.

[hard timber]

K

Would theta be 90 degrees?

[willow pecan]

Well, obviously not.

[hard timber]

Oh

I’m a bit lost sorry

[willow pecan]

Well, θ and the given angle are supplementary angles.

[eternal pawn]

Supplementary meaning that they add up to 180 degrees

[hard timber]

So theta is 55 degrees?

[willow pecan]

Yes.

[eternal pawn]

Yeps

[willow pecan]

We should probably denote the known quantities by something.

Like this, maybe. So, we know a, b, α and want to find r.

[hard timber]

I see

I’ll use tan right?

[willow pecan]

Yes, since you know one lateral side and want to find the other one.

[hard timber]

Perfect

I’ve worked out that X is 28.56

[willow pecan]

Well, let's solve this generally first.

[hard timber]

Sorry I don’t understand

[willow pecan]

In terms of the quantities we denoted: a, b, α.

[hard timber]

Do I solve the other triangle?

[willow pecan]

What do you mean? You're doing the correct thing.

We just want to solve generally first. So, x = a tan(θ).

[hard timber]

Do I now solve the whole thing?

Like add A and B together to get that big adjacent, then solve the whole triangle using something

[willow pecan]

Yeah. Considering it's a right triangle, it's not hard to guess what to use.

[hard timber]

Sorry but what do I use?

[willow pecan]

Well, you know two sides of a right triangle and want to know the third side.

[hard timber]

Oh I see

Gotta solve the hypotenuse?

[willow pecan]

Yes.

[hard timber]

I can use cos right?

I’ve tried to use sin and cos but it comes up with 0.02

Wit a minute

I don’t use sin cos or tan

[willow pecan]

For what?

[hard timber]

Yea nvm

[willow pecan]

You can just use Pythagoras's theorem.

[hard timber]

Yea

I did that and got 34.87

[willow pecan]

Hold on, let me check.

Oh, wait, definitely not.

[hard timber]

Oh

[willow pecan]

Your hypotenuse turned out to be smaller than one of the sides.

Of course, that's impossible.

[hard timber]

You sure it’s smaller?

[willow pecan]

I mean, the given side is 50 cm...

So yeah.

What formula did you get?

[willow pecan]

Oh, I see your mistake.

You took one of the sides in the theorem to be 20 cm instead of (20 + 30) cm = 50 cm.

[hard timber]

Oh I see that now

Yea coz the hypotenuse is the opposite of the other triangle

Is it?

[willow pecan]

Yeah, the big one.

[hard timber]

Yea

But do I need to figure out what that hypotenuse is?

[willow pecan]

As I said, your only mistake is taking the bottom side as 20 cm instead of 50 cm.

So, just replace that in the formula you got.

[hard timber]

Ok

I got 57.58

[willow pecan]

Yeah, nice! Don't forget about units, though.

[hard timber]

57.68 cm?

[willow pecan]

57.58 cm, rather. But yeah.

[hard timber]

Oh yea I meant to say that

So now I just use Pythagorus ?

[willow pecan]

What do you mean? You're done, you found r.

[hard timber]

Oh I did

Oh wow

Thank you

[willow pecan]

You're welcome!

[hard timber]

I just gotta remember this