I will attach the files on the chat

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 = 28.309 feet
Length of the...