The approximate length of minor arc XZ is about 3.7 meters
Further explanation
The basic formula that need to be recalled is:
Circular Area = π x R²
Circle Circumference = 2 x π x R
where:
R = radius of circle
The area of sector:
[tex]\text{Area of Sector} = \frac{\text{Central Angle}}{2 \pi} \times \text{Area of Circle}[/tex]
The length of arc:
[tex]\text{Length of Arc} = \frac{\text{Central Angle}}{2 \pi} \times \text{Circumference of Circle}[/tex]
Let us now tackle the problem!
Given:
Radius of Circle = R = 3 m
Central Angle = 70°
Unknown:
Length of Minor Arc = ?
Solution:
[tex]\text{Length of Arc} = \frac{\text{Central Angle}}{360^o} \times \text{Circumference of Circle}[/tex]
[tex]\text{Length of Arc} = \frac{{70}^o}{360^o} \times {2 \pi (3)}[/tex]
[tex]\text{Length of Arc} = \frac{7}{36} \times {6 \pi}[/tex]
[tex]\text{Length of Arc} = \frac{7}{6}\pi[/tex]
[tex]\text{Length of Arc} \approx 3,7 \texttt{ meters}[/tex]
The closest option available will be option B. 3.7 meters
[tex]\texttt{ }[/tex]
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Answer details
Grade: College
Subject: Mathematics
Chapter: Trigonometry
Keywords: Sine , Cosine , Tangent , Opposite , Adjacent , Hypotenuse, Circle , Arc , Sector , Area, Inches , Frisbee , Diameter , Radius , Trigonometry ,
