Respuesta :
Answer:
26
Step-by-step explanation:
The formula should be
s=[tex]\frac{104}{360}[/tex]2[tex]\pi[/tex]r
If 90 inches is the full diameter, cutting it by half will give you the radius, then you just plug in everything else.
[tex]\frac{104}{360}[/tex]*2*[tex]\pi[/tex]*45= 26[tex]\pi[/tex] inches
This answer is better to leave it as pie, so multiply everything else besides the pie.
In circle U , VT = 90 inches. T U, Z U, and V U are radii. Angle Z U V is 104 degrees. the length of arc ZV will be 26 in.
How to find the relation between angle subtended by the arc, the radius and the arc length?
[tex]2\pi^c = 360^\circ = \text{Full circumference}[/tex]
The superscript 'c' shows angle measured is in radians.
If radius of the circle is of r units, then:
[tex]1^c \: \rm covers \: \dfrac{circumference}{2\pi} = \dfrac{2\pi r}{2\pi} = r\\\\or\\\\\theta^c \: covers \:\:\: r \times \theta \: \rm \text{units of arc}[/tex]
In circle U , VT = 90 inches.
T U, Z U, and V U are radii. Angle Z U V is 104 degrees.
We want to find the length of arc ZV
The formula should be
[tex]s = \dfrac{104}{360} 2\pi r[/tex]
If 90 inches is the full diameter, the half will give you the radius,
[tex]s = \dfrac{104}{360} \times 2\times 3.14 \times 45[/tex]
s = 26 inches
Learn more about angle, arc length relation here:
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