Answer:
3.5 cm
Step-by-step explanation:
Length of an arc is a "part" of the circumference of a circle.
The circumference is the perimeter of the circle. Formula is:
[tex]C=\pi d[/tex]
Where
C is circumference
d is diameter
Given diameter is 16, the circumference would be:
[tex]C=\pi (16)\\C=16\pi\\C=50.27[/tex]
Now, the arc is 25 degrees, which is 25/360 th of the circle's circumference [recall, there is 360 degrees in whole circle].
So, we multiply the circumference we got by (25/360) to get our answer:
[tex]\frac{25}{360}*50.27=3.5[/tex]
Minor Arc JH = 3.5 cm
To solve the problem we need to know about the length of the Arc.
we know that the length of an arc of a circle is given by the formula,
[tex]\bold{Length\ of\ the\ Arc = \theta\times (\dfrac{\pi}{180})\times r}[/tex],
where, r is the radius of the circle and θ is the angle for which the arc is been formed from the center in degree.
The approximate length of minor arc JH, Round to the nearest tenth of a centimeter is 3.5 cms.
Given to us,
Radius of circle, r = [tex]\bold{\dfrac{Diameter}{2} =}[/tex] [tex]\bold{\dfrac{16}{2} = 8\ cm}[/tex] ,
We know that when two lines cross each other forming four angles, such that, each pair of opposite angles are equal to each other. This pair of angles are known as Vertical opposite angles.
Similarly, ∠KML = ∠JML = 25°.
Substituting the values in the formula of the length of the arc,
length of the arc JH = [tex]\bold{\theta\times (\dfrac{\pi}{180})\times r}[/tex]
= [tex]25 \times\dfrac{\pi}{180}\times 8[/tex]
= 3.49 cm
Therefore, the length of the arc is 3.49 cms. rounding of to tenth place we get the value as 3.5 cm. , as the last digit is 9 rounding off to the next number.
Hence, the approximate length of minor arc JH, Round to the nearest tenth of a centimeter is 3.5 cms.
Learn more about Arc:
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