Results 1 to 2 of 2

Math Help - Help with a circle problem

  1. #1
    Junior Member
    Joined
    Jan 2007
    Posts
    35

    Exclamation Help with a circle problem

    In the following figure, P is the center of the circle, which has a radius of 5 feet. The arc length AB is 10 feet. Find the distance AB Estimate to two decimal places.(Picture Attached) Any help appreciated.
    Attached Thumbnails Attached Thumbnails Help with a circle problem-circle.jpg  
    Follow Math Help Forum on Facebook and Google+

  2. #2
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by leviathanwave View Post
    In the following figure, P is the center of the circle, which has a radius of 5 feet. The arc length AB is 10 feet. Find the distance AB Estimate to two decimal places.(Picture Attached) Any help appreciated.
    recall that s = rA where s is the arclength, r is the radius and A is the angle of the segment we're concerned with in radians (there's a different formula if you want to work in degrees).

    => A = s/r = 10/5 = 2 radians
    now note that ABP forms an isoseles triangle, with base AB. we can find the length of AB using the Law of Cosines

    AB^2 = AP^2 + BP^2 - 2AP*BPcosP
    => AB^2 = 5^2 + 5^2 - 2*5*5cos2 ....remember to put your calculator in radian mode

    => AB^2 = 50 - 50(-0.41615) = 70.8
    => AB = 8.41 approximately

    I rounded off some when I was calculating so if you want a more "accurate" answer, redo the procedure with more decimal places


    if you want to work in degrees, use the formula l = A/360 * 2pi*r where l is the arclength and A is the angle, and then use the Cosine rule for the length of the line once more (this time with your calculator in degrees mode).
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Circle problem
    Posted in the Pre-Calculus Forum
    Replies: 6
    Last Post: December 18th 2010, 06:05 AM
  2. Circle Problem
    Posted in the Geometry Forum
    Replies: 1
    Last Post: November 13th 2010, 01:39 PM
  3. Circle Problem
    Posted in the Geometry Forum
    Replies: 2
    Last Post: November 8th 2010, 04:40 PM
  4. Circle Problem
    Posted in the Geometry Forum
    Replies: 2
    Last Post: May 7th 2010, 01:20 AM
  5. circle problem
    Posted in the Geometry Forum
    Replies: 8
    Last Post: April 23rd 2010, 11:13 AM

Search Tags


/mathhelpforum @mathhelpforum