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For the problem below, [tex]\theta[/tex] is a central angle in a circle of radius [tex]r[/tex]. Find the length of arc [tex]s[/tex] cut off by [tex]\theta[/tex]. Do not round your answer.

Given:
[tex]\theta = 2.3 \text{ radians}[/tex]
[tex]r = 2.2 \text{ feet}[/tex]

[tex]s = \square \text{ feet}[/tex]

Sagot :

GinnyAnsweridn
To find the length of arc [tex]\( s \)[/tex] cut off by the central angle [tex]\( \theta \)[/tex] in a circle with radius [tex]\( r \)[/tex], we can use the formula:

[tex]\[ s = r \cdot \theta \][/tex]

where:
- [tex]\( s \)[/tex] is the length of the arc,
- [tex]\( r \)[/tex] is the radius of the circle,
- [tex]\( \theta \)[/tex] is the central angle in radians.

Given:
- [tex]\( \theta = 2.3 \)[/tex] radians,
- [tex]\( r = 2.2 \)[/tex] feet,

we can now substitute these values into the formula to find the length of the arc [tex]\( s \)[/tex].

[tex]\[ s = 2.2 \cdot 2.3 \][/tex]

Upon multiplying these values, the length of the arc [tex]\( s \)[/tex] is found to be:

[tex]\[ s = 5.06 \text{ feet} \][/tex]

Thus, the length of arc [tex]\( s \)[/tex] is 5.06 feet.
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