On a circle of radius 7 feet, what angle would subtend an arc of length 1 feet? In radians: In degrees: degrees
On a circle of radius 7 feet, what angle would subtend an arc of length 1 feet? In radians: In degrees: degrees
Trigonometry (MindTap Course List)
8th Edition
ISBN:9781305652224
Author:Charles P. McKeague, Mark D. Turner
Publisher:Charles P. McKeague, Mark D. Turner
Chapter7: Triangles
Section: Chapter Questions
Problem 1GP
Related questions
Question
7.1,4
![**Question:**
Given a circle with a radius of 7 feet, what angle (in radians and in degrees) would subtend an arc of length 1 foot?
**Answer:**
In radians: [Input Box]
In degrees: [Input Box] degrees
**Explanation:**
To find the angle subtended by an arc of length \(s\), given the radius \(r\) of the circle, we can use the formula for the angle in radians:
\[
\theta = \frac{s}{r}
\]
In this case:
\[
\theta = \frac{1 \text{ foot}}{7 \text{ feet}} = \frac{1}{7} \text{ radians}
\]
To convert this angle from radians to degrees, we use the conversion factor \(180^\circ = \pi\) radians:
\[
\theta \text{ (in degrees)} = \theta \text{ (in radians)} \times \frac{180^\circ}{\pi}
\]
So,
\[
\theta \text{ (in degrees)} = \frac{1}{7} \times \frac{180^\circ}{\pi}
\]
Simplifying this will give the angle in degrees.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4d6261b1-d641-4c15-8b49-7d4d38863372%2Ff68f1600-5367-40b7-a79f-4b0ecf859249%2Fgfrsq37_processed.png&w=3840&q=75)
Transcribed Image Text:**Question:**
Given a circle with a radius of 7 feet, what angle (in radians and in degrees) would subtend an arc of length 1 foot?
**Answer:**
In radians: [Input Box]
In degrees: [Input Box] degrees
**Explanation:**
To find the angle subtended by an arc of length \(s\), given the radius \(r\) of the circle, we can use the formula for the angle in radians:
\[
\theta = \frac{s}{r}
\]
In this case:
\[
\theta = \frac{1 \text{ foot}}{7 \text{ feet}} = \frac{1}{7} \text{ radians}
\]
To convert this angle from radians to degrees, we use the conversion factor \(180^\circ = \pi\) radians:
\[
\theta \text{ (in degrees)} = \theta \text{ (in radians)} \times \frac{180^\circ}{\pi}
\]
So,
\[
\theta \text{ (in degrees)} = \frac{1}{7} \times \frac{180^\circ}{\pi}
\]
Simplifying this will give the angle in degrees.
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