For a circle with a radius of 15 cm, what is the length of an arc intercepted by an angle measuring 120°?

31.43 cm

Step-by-step explanation:

The length of an arc  is calculated using the formula:

X 2r

where : theta is the angle in degree

r = radius

If the angle is given in Radian , the length can be calculated using the formula:

L = r∅

Since , the angle is given in degree , we will use the first formula.

L = X 2r

L = X 2 X π X 15

L = X 2 X X 15

L =

L = 31.42857143

L ≈ 31.43 cm

there are lots of ways.   pick's theorem tells us if the vertices are lattice points the area a is

a = b/2 + i - 1

where b is the number of boundary lattice points and i is the number of interior lattice points.

in the figure i count b=16, i=50 so

a = 8 + 50 - 1 = 57

let's try the shoelace formula.   the area is half the sum of the cross products of the sides.  

a(-2,6)   -2(2)-6(-5) = 26

b(-5,2)   -5(-3) - 2(-2) = 19

c(-2,-3) -2(-3) - (-3)(4) = 18

d(4,-3)   4(3) - (-3)(5) = 27

e(5,3)   5(3) - 3(1) = 12

f(1,3)     1(6) - 3(-2) = 12

a(-2,6)

each of the cross products is twice the area of the triangle with the associated side and one vertex the origin. so the area of abo=26/2=13.

area = (1/2) (26 + 19 +   18 + 27 + 12 + 12) = 57

that checks!

step-by-step explanation:

answers available in this download

(pearson%2c%25202012)%2520bbs.pdf& usg=aovvaw1obmtxnfghfgxhx0urh_je