# Trigonometry

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Gabe is spending two weeks on an archaeological dig. He finds a fragment of a circular plate that his leader thinks may be valuable. The arc length of the fragment is about 1/6 the circumference of the original complete plate and measures 1.65 inches. A similar plate found earlier has a diameter of 3.14 inches.

Could Gabe's fragment match this plate?

How long would the arc length of a fragment be if it were 1/6 the circumference of the plate?

I have no idea how to start these.

• Trigonometry -

(1/6)(pi d) =1.65
d = 1.65 (6/pi) = 3.15

• Trigonometry -

Thanks - and then there's one more if you don't mind.
Toby finds another fragment of arc length 2.48 inches. What fraction of the outer edge of Gabe's plate would it be if this fragment were part of Gabe's plate?

1/4
1/2
2/3
3/4

• Trigonometry -

d = 3.14
pi d = 9.864
2.48 / 9.864 = .251
a quarter of it

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