Include explanation because im stuck

We need to use law of sin

sin A/a = sin B/b

a is a side opposite to the angle A,

b is a side opposite to the angle B.

We can write

sin 75⁰/22 = sin x/12

sin x = (12*sin 75⁰)/22

x= sin⁻¹((12*sin 75⁰)/22≈ 31.8⁰

x ≈ 31.8⁰

I used the Law of Sines to find this. I set sin75/22 equal to sinx/12. I then multiplied both sides by 12 and got 12sin75/22 is equal to sinx. I then solved 12sin75/22 to get 0.56868 is equal to sinx. I then did sine inverse on both sides to get that the angle of x is about 31.79 degrees.

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!

he will have 300 because he is really broke and 300 is in his imangine

step-by-step explanation: he ehe heh step by the thy