Question

The angle lies at the center of a circle and subtends an arc of the circle. Find the missing angle measure, circle radius, or arc length. $$ \begin{array}{ccc} \text { Angle } & \text { Radius } & \text { Are Length } \\ ? & 14 & 7 \end{array} $$

Name: Problem 3, Chapter 1: Calculus: Graphical, Numerical, Algebraic
Uploaded: 2021-09-02T01:03:02-08:00
Duration: 23 s
Channel: Erika Bustos
Description: The angle lies at the center of a circle and subtends an arc of the circle. Find the missing angle measure, circle radius, or arc length. Angle Radius Are Length ? 14 7

   The angle lies at the center of a circle and subtends an arc of the circle. Find the missing angle measure, circle radius, or arc length.
$$
\begin{array}{ccc}
\text { Angle } & \text { Radius } & \text { Are Length } \\
? & 14 & 7
\end{array}
$$

Calculus: Graphical, Numerical, Algebraic

Ross L. Finney,… 5th Edition

Chapter 1, Problem 3

Instant Answer

Solved by Expert Erika Bustos

09/02/2021

Step 1

We can use the formula for the length of an arc of a circle, which is given by s = rθ, where θ is in radians. Show more…

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The angle lies at the center of a circle and subtends an arc of the circle. Find the missing angle measure, circle radius, or arc length. $$ \begin{array}{ccc} \text { Angle } & \text { Radius } & \text { Are Length } \\ ? & 14 & 7 \end{array} $$

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Key Concepts

Radians

Radians are a unit of angular measure used in mathematics, particularly in relation to circles. One radian is the angle for which the length of the arc is equal to the radius of the circle. Understanding radian measure is essential for using the arc length formula correctly, as the formula s = r * ? requires the angle to be in radians.

Arc Length Formula

This concept refers to the formula that relates the arc length of a circle to the radius and the central angle it subtends. The formula is s = r * ?, where s is the arc length, r is the radius, and ? is the central angle in radians. This formula is fundamental in problems involving parts of a circle.

Central Angle

The central angle is the angle subtended at the center of the circle by an arc or chord. It is crucial in determining the portion of the circle that the arc represents. The measure of this angle, when given in radians, can be directly used in the arc length formula.

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