please step by step instructions

If s denotes the length of the arc of a circle of radius r subtended by a central angle θ, find the missing quantity.r = 13.9 inches, θ = 150°, s = ?

A) 36.6 in.B) 36.7 in.C) 36.5 in.D) 36.4 in.

WYZANT.COM
CREATE FREE ACCOUNT
Sign In

Access thousands of free resources from expert tutors

Comment on posts and interact with the authors

Ask questions and get free answers from tutors

View videos, take interactive quizzes, and more!

please step by step instructions

If s denotes the length of the arc of a circle of radius r subtended by a central angle θ, find the missing quantity.r = 13.9 inches, θ = 150°, s = ?

A) 36.6 in.B) 36.7 in.C) 36.5 in.D) 36.4 in.

Tutors, please sign in to answer this question.

Belia,

Let's start by thinking about what we know about a circle.

1) Circumference C = 2(Pi)D

2) Total Angle in a circle is 360 degrees

Since they gave you theta, just figure out what fraction of the total angle of the circle this is: 150/360 = .4167

Then calculate the Total Circumference of the Circle = 2(3.14)(13.9) = 87.3

So the arc length is (.4167) * (87.3) = 36.38 which rounds to 36.4

Does that make sense? If not post a follow-up comment and we'll go from there.

Paul

Circumference of circle:

C = (pi)*D = 2*(pi)*r = 2*(pi)*13.9 inches = 87.336 onches

(150°)/(360°) = 5/12

Hi Bella,

The formula for finding the length of an arc is: s = Rθ, where θ is the central angle in radians.

The formula for finding the length of an arc is: s = Rθ, where θ is the central angle in radians.

150^{o} = (150/180)∏ ≈ 2.62 radians

Therefore,

s = (2.62)(13.9) ≈ **36.4**

Hope this helps!

The length of an arc is simply l=r*θ*π/180, where θ is in degrees, π≈3.1415926

To understand where this formula came from, recall that the total circumference of a circle is 2πr. The complete circle is 360 degrees, so the arc subtended by 1 degree central angle is simply 2πr/360 or πr/180. Then if the central angle is θ degrees,
the arc length is:

l=πr/180*θ;

In your case, l≈3.14*13.9*150/180=3.14*13.9*5/6≈36.4 in.

- Algebra 1 631
- Algebra 2 488
- Math 1332
- Geometry 262
- Precalculus 102
- Prealgebra 37
- Calculus 166
- SAT Math 1
- Math Help 593
- Trig 39