Geometry question. Please help! Giving medal :)

Question

anonymous · Answer

attachment

mathstudent55 · Answer

The angle measure of an arc is the same as the measure of its central angle.

mathstudent55 · Answer

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mathstudent55 · Answer

What is the measure of angle x and arc x?
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anonymous · Answer

150?

mathstudent55 · Answer

Good.
Now you know the angle measure of the arc whose length you need is 150 deg.
Now we move on to the arc lenght part.

mathstudent55 · Answer

The circumferece of a circle is $C = \pi d$.
The arc length is a portion of the circumference.

mathstudent55 · Answer

A circle is an arc of $360^o$ measure.
An arc of n degrees is a fraction, $ \dfrac{n}{360^o} $, of the entire circle.
The length of an arc is:

$S = \dfrac{n}{360^o} \pi d$

Here, $n = 150^o$, $d = 36 ~cm$

Plug in the values you have for n and d, and find S. Remember to leave S in terms of $ \pi$.

anonymous · Answer

i got 47.1. i don't understand how to leave s in terms of pi..

anonymous · Answer

@mathstudent55

mathstudent55 · Answer

It's easier than you think. Plug in the numbers and keep $\pi$ there without using 3.14 or another approximation. Keep $\pi$ as if it were a variable.

S = \dfrac{n}{360^o} \pi d

$S =\dfrac{150^o}{360^o} \pi (36) $

$S = 15 \pi $

anonymous · Answer

good job you got it
I am of no help here :(

anonymous · Answer

thank you so much @mathstudent55 :)

mathstudent55 · Answer

You're welcome. Good job!