A circle's center is at $(4, 7)$ $(4 ,7 )$ and it passes through $(9, 1)$ $(9 ,1 )$ . What is the length of an arc covering $\frac{5 π}{3}$ $(5pi ) /3$ radians on the circle?

Question

A circle's center is at $(4, 7)$ $(4 ,7 )$ and it passes through $(9, 1)$ $(9 ,1 )$ . What is the length of an arc covering $\frac{5 π}{3}$ $(5pi ) /3$ radians on the circle?

1 Answer

Impact of this question

1459 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-08-13T13:03:21

Length of the Arc $≅ 41$ $~=41$

Explanation:

Circle's center is at $(4, 7)$ $(4,7)$ and it passes through $(9, 1)$ $(9,1)$
Therefore Length of the $r a d i u s = r$ $radius=r$ =Distance between these points $(4, 7) and (9, 1)$ $(4,7) and (9,1)$
or
$r a d i u s = r = \sqrt{{(9 - 4)}^{2} + {(7 - 1)}^{2}}$ $radius =r=sqrt((9-4)^2+(7-1)^2)$
$= \sqrt{5^{2} + 6^{2}}$ $=sqrt(5^2+6^2)$
$= \sqrt{25 + 36}$ $=sqrt(25+36)$
$= \sqrt{61}$ $=sqrt61$
$= 7.81$ $=7.81$
Therefore Circumfernce of the Circle $= 2 π r = 2 π \times 7.81 ≅ 49$ $=2pir=2pitimes7.81~=49$
Arc covers $\frac{5 π}{3}$ $(5pi)/3$ radians on the Circle
In other words Arc covers $\frac{5 π}{3} \div 2 π = \frac{5}{6} \times$ $(5pi)/3-:2pi=5/6times$ (circumference of the Circle)
Therefore Length of the Arc $= \frac{5}{6} \times 2 π r = \frac{5}{6} \times 49 ≅ 41$ $=5/6 times2pir=5/6 times49~=41$

Science

Math

Humanities

... and beyond

A circle's center is at $(4, 7)$ $(4 ,7 )$ and it passes through $(9, 1)$ $(9 ,1 )$ . What is the length of an arc covering $\frac{5 π}{3}$ $(5pi ) /3$ radians on the circle?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

A circle's center is at (4,7)(4 ,7 ) and it passes through (9,1)(9 ,1 ). What is the length of an arc covering 5π3(5pi ) /3 radians on the circle?

1 Answer

Explanation:

Related questions

Impact of this question

A circle's center is at $(4, 7)$ $(4 ,7 )$ and it passes through $(9, 1)$ $(9 ,1 )$ . What is the length of an arc covering $\frac{5 π}{3}$ $(5pi ) /3$ radians on the circle?