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Robert · Accepted Answer

PART1 
1) Find the arc length and the area between the points (5,0) and (3,2) on the 
circle centered at (3,0) 
 
Let θ be the angle formed at the centre by the points (5,0) and (3,2) 
cos θ=
        
   
 
here a=b=r =2 and c= distance between (5,0) and (3,2) 
c=((5-3)2+(0-2)2)0.5 = (8)0.5 
 cos θ=
        
   

     
     => θ = 90O 
 Arc length =
 
    

    
             units 
 Area = 
 
    

    
         unit2
2) What angle corresponds to 10ᴨ% of the area of a circle? 
Area of a sector = 
 
    

   
        => θ =
   
      
 θ = 
   
   
      = 113.14 degrees.
3)
 
Point D is 15 feet above the ground. 
Now the length BD: 
ADE form a right angled triangle with 90O at E and DE = 15-3=12feet and 
AE=10-3 = 7feet 
Now AD2 = AE2+DE2 => AD = (193)0.5 feet = 13.892feet 
tanA = DE/AE = (12/7) 
ABC form a right angled triangle with 90O at B since ABD is a tangent to the 
circle (spool) and BC=r=1foot 
tanA = BC/AB = (12/7) => AB =(7/12)feet =0.583feet 
=>BD = AD-AB = 13.892 – 0.583 =13.309 feet 
=> Length of the thread required = BD+15feet = 28.

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