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[shadow drift]

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[unreal hearth]

Here are the given parameters visualized.
If we know R and θ, how can we find r? Try looking at what you know about the upper right triangle.

[marsh lichen]

r = root 3?

[unreal hearth]

No, forget about the values for now.

[marsh lichen]

is the answer 2pi root3?

[marsh lichen]

okay

[marsh lichen]

we know the

height

and hypotenus

[unreal hearth]

Rather, we know the hypotenuse and the angle between it and the unknown side.

[marsh lichen]

i dont understand 😭

[unreal hearth]

Note that the two radii are parallel. So, the angle in the upper right triangle is also θ.
So, if we know the angle and an adjacent side, which trigonometric function should we use?

[marsh lichen]

cos?

[unreal hearth]

Yes.

[marsh lichen]

oooo

so

[unreal hearth]

So, what is cos(θ)?

[marsh lichen]

cos30

[marsh lichen]

b/h

[unreal hearth]

No-no, as I said, forget about values for now.

[marsh lichen]

oh okayy

[unreal hearth]

For this triangle, what is cos(θ)?

[marsh lichen]

r/R

[unreal hearth]

Right.

Now, try multiplying the top and bottom of r/R by 2π.

[marsh lichen]

2πr/2πR

ohhh

now i do

[unreal hearth]

Yes.
And now notice that those are just P(base) and P(cross-section).

[marsh lichen]

cos(30)=2πr/66

so

[unreal hearth]

You don't need r.

[marsh lichen]

2πr= cos(30)*60

[unreal hearth]

You need P(cross-section).

[marsh lichen]

crosssection?

ohhh

[unreal hearth]

We get:
cos(θ) = P(cross-section)/P(base)
Thus:
P(cross-section) = P(base)cos(θ)

[marsh lichen]

R?

[unreal hearth]

And now you can substitute P(base) and θ.

[marsh lichen]

which is the cross section 😭

[unreal hearth]

It's a surface that you get when you cut a body with a plane...

[marsh lichen]

whats a cross section

[marsh lichen]

ohhhh

that bottom thing?

[unreal hearth]

I mean, that's what you're asked to find the perimeter of.

[marsh lichen]

ohhhh

[unreal hearth]

Well, yes, but we're interested in the upper one.

[marsh lichen]

sooo

is it

10.38?

i out it in my calculator

and got that ans

[unreal hearth]

No.

Also, no need to use a calculator for now.

Let's find the exact value first.

[marsh lichen]

okayy

[unreal hearth]

So, what is it?

[marsh lichen]

idk 😭

i got confused

[unreal hearth]

We have:
P(cross-section) = P(base)cos(θ)
We have P(base) = 66 cm, θ = 30°. So, what will P(cross-section) be?

[marsh lichen]

ohhhh

66 * cos(30)

66 * root(3)/2

33 * root(3)

33 * 1.732

57?

[unreal hearth]

Well, 33√(3) cm, yes. After that, you can use a calculator.

And yeah, it's around 57 cm.

So, what option do we pick?

[marsh lichen]

55

thank you so muchh

[unreal hearth]

Yup.