What's the area of the sector of a circle if the radius is 18 in and the central angle is 172°? in
Angles in Circles
Angles within a circle are feasible to create with the help of different properties of the circle such as radii, tangents, and chords. The radius is the distance from the center of the circle to the circumference of the circle. A tangent is a line made perpendicular to the radius through its endpoint placed on the circle as well as the line drawn at right angles to a tangent across the point of contact when the circle passes through the center of the circle. The chord is a line segment with its endpoints on the circle. A secant line or secant is the infinite extension of the chord.
Arcs in Circles
A circular arc is the arc of a circle formed by two distinct points. It is a section or segment of the circumference of a circle. A straight line passing through the center connecting the two distinct ends of the arc is termed a semi-circular arc.
Round the answer to the hundredth place.
![**Problem Statement:**
Find the area of a sector of a circle if the radius is 18 inches and the central angle is 172 degrees.
**Solution:**
To find the area of a sector, we use the formula:
\[
\text{Area of sector} = \frac{\theta}{360} \times \pi r^2
\]
where:
- \(\theta\) is the central angle in degrees,
- \(r\) is the radius of the circle.
Given:
- \(\theta = 172^\circ\),
- \(r = 18\) inches.
Calculate the area of the sector:
1. Plug the values into the formula:
\[
\text{Area of sector} = \frac{172}{360} \times \pi \times (18)^2
\]
2. Simplify the calculation:
\[
\text{Area of sector} = \frac{172}{360} \times 3.1416 \times 324
\]
3. Continue with arithmetic to find the final result.
The area of the sector will be displayed in the box in \(\text{in}^2\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6ed323b9-8e35-4824-8e78-fcaf55c6ad57%2F141ec6b3-78c6-446d-8578-ef7ec2966c40%2Fh017nr_processed.jpeg&w=3840&q=75)
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