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Here is the complete question.
[tex]Consider \ circle \ Y \ with \ radius \ 3 m \ and \ central \ angle \ XYZ \ measuring \ 70°. \\ \\ What \ is \ the \ approximate \ length \ of \ minor \ arc \ XZ?\\ \\ Round \ to \ the \ nearest \ tenth \ of \ a \ meter. \\ 1.8 meters \\ 3.7 \ meters \\ 15.2\ meters \\ 18.8 \ meters[/tex]
Answer:
3.7 meters
Step-by-step explanation:
From the given information:
The radius is 3m
The central angle XYZ = 70°
To calculate the circumference of the circle:
C = 2 π r
C = 2 × 3.142 × 3
C = 18.852 m
Let's recall that:
The circumference length define a central angle of 360°
The approximate length of minor arc XZ can be determined as follow:
Suppose the ≅ length of minor arc XZ = Y
By applying proportion;
[tex]\dfrac{18.852}{360} = \dfrac{Y}{70}[/tex]
Y(360) = 18.852 × 70
Y = 1319.64/360
Y = 3.66
Y ≅ 3.7 m