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Mathematics, 22.06.2019 21:00 AdoNice

For a circle with a diameter of 6 meters, what is the measurement of a central angle (in degrees) subtended by an arc with o length of 7 3 π meters?

Answers

ansver
Answer from: thatcommondumbgirl

140

Step-by-step explanation:

If it is an arc of 7pi/3, and the circumference is 6*pi or 6pi, then the arc takes up 7/18 of the circle, and since a circle has 360 degrees, the answr is 7/18 * 360 or 140.

ansver
Answer from: Shavaila18

..............................


For a circle with a diameter of 6 meters ,what is the measurement of a central angle (in degrees) su
ansver
Answer from: andrewcassity1

\boxed{\boxed{\theta=150^{\circ}}}

Step-by-step explanation:

We know that,

\text{Arc length}=r\cdot \theta

where,

r = radius,

θ = central angle in radian.

Given,

diameter = 6 m, so radius = 3 m.

\text{Arc length}=\dfrac{5}{2}\pi

Putting the values,

\Rightarrow \dfrac{5}{2}\pi=3\theta

\Rightarrow \theta=\dfrac{5}{2\times 3}\pi

\Rightarrow \theta=\dfrac{5}{6}\pi=\dfrac{5}{6}\times 180^{\circ}=150^{\circ}

ansver
Answer from: yedida

Answer : The measurement of a central angle is, 140^o

Step-by-step explanation :

Formula used for angle subtended by an arc is:

s=\frac{\pi r\theta}{180}

where,

s = arc length = \frac{7}{3}\pi m

r = radius = \frac{diameter}{2}=\frac{6m}{2}=3m

Now put all the given values in the above formula, we get:

s=\frac{\pi r\theta}{180}

\frac{7}{3}\pi=\frac{\pi \times (3)\times \theta}{180}

\theta =140^o

Thus, the measurement of a central angle is, 140^o

ansver
Answer from: yeetusbobeetus

the answer is (D)

Step-by-step explanation:

ansver
Answer from: vcornejo7

The measurement of a central angle (in degrees) subtended by an arc is 150^{\circ \:}\:\:.

Step-by-step explanation:

as

d= 6 meters

so

r= 3 meters

and

Arc=\frac{5}{2}\pi meters

Using the formula

\:Arc\:=r\:\theta

\:\frac{5}{2}\pi =3\theta

\mathrm{Switch\:sides}

3\theta =\frac{5}{2}\pi \:

\mathrm{Multiply\:fractions}:\quad \:a\cdot \frac{b}{c}=\frac{a\:\cdot \:b}{c}

3\theta =\frac{5\pi \:}{2}

\mathrm{Divide\:both\:sides\:by\:}3

\frac{3\theta \:}{3}=\frac{\frac{5\pi \:}{2}}{3}

Simplify

\theta \:=\frac{5\pi \:}{6}

\theta \:=\frac{5\left(180^{\circ }\right)\:}{6}

\theta \:=150^{\circ \:}\:\:

Therefore, the measurement of a central angle (in degrees) subtended by an arc is 150^{\circ \:}\:\:.

ansver
Answer from: alleahbethea199

The measurement of the angle subtended by an arc with a length of 5/2 pi meters is 149.542°

Step-by-step explanation:

Here, the diameter of the circle = 6 m

Diameter = 2 x RADIUS

So, radius  = D / 2  = 6 / 2  = 3 m

Also, the length of the arc = ( \frac{5}{2}  \pi) meters

Putting π  = 3.14, we get  

The length S of the arc = \frac{5}{2}  \times (3.14)  =  7.85  

or, S  = 7.85 m

Let us assume the arc subtends angle Ф at the center of the circle.

⇒  S  = r Ф

or, Ф = \frac{S}{r}   = \frac{7.85}{3}  =  2.61

⇒Ф  = 2.61 radians

Now, 1 Radian  = 57.2958 Degrees

⇒ 2. 62 Radian  = 2.61  x  ( 57.2958 Degrees)  =  149.542 °

or, Ф    =  149.542°

Hence, the measurement of the angle subtended by an arc with a length of 5/2 pi meters is 149.542°

ansver
Answer from: cvhufjbvbcxx9845
Arc length = (5/2) * PI meters = 7.853981634 meters
circle circumference = 2 * PI * radius = 2 *PI * 3
18.8495559215
arc length = (7.85381634 / 18.8495559215) * 360 = 
0.4166578975 *360 =
150 degrees
ansver
Answer from: shikiaanthony
Arc length is given by:
C=θ/360πd
thus plugging in the values we get:
5/2π=θ/360π*6
dividing through by 6π we get:
5/12=θ/360
multiplying both sides by 360
θ=150°
ansver
Answer from: donalyndearingbizz
Arc length=5/2 pi
diameter=6m
Circumference=pi x d=pi x 6m= 6pi

Circumference/arc length=6pi/(5/2pie)=360degree/central angle

6pie x central angle=360degree x 5/2pie

Central angle=360degree x 5/2pie/6pie

Central angle=360degree x 5/12

Central angle=150degree

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