Find the measure of an arc in radians if the radius of the arc is 2.3 inches and the length of the arc is 3.887 inches. radians (round answer to two decimal places)
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.
What would the measure of the arc be with the given values?
![**Problem Statement:**
Find the measure of an arc in radians if the radius of the arc is 2.3 inches and the length of the arc is 3.887 inches.
**Answer Box:**
\[ \boxed{\phantom{0}} \text{ radians} \]
(Round answer to two decimal places)
**Explanation:**
To find the measure of an arc in radians, use the formula:
\[ \theta = \frac{s}{r} \]
where:
- \( \theta \) is the measure of the arc in radians,
- \( s \) is the length of the arc,
- \( r \) is the radius of the circle.
Given:
- \( s = 3.887 \) inches,
- \( r = 2.3 \) inches.
So, the measure of the arc in radians is:
\[ \theta = \frac{3.887}{2.3} \]
Calculating this will give the value of \( \theta \), which should then be rounded to two decimal places.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F346b36e0-a4d8-47d7-8bd1-1ad776cb1cf3%2F8f2aa441-f747-45e1-b10e-8cf6b7bd724e%2Ft64houq_processed.png&w=3840&q=75)
Step by step
Solved in 2 steps with 2 images
