Can someone me? how do i solve for the exact value?

sin(α + β) = sin(α) cos(β) + cos(α) sin(β)

sin(α – β) = sin(α) cos(β) – cos(α) sin(β)

These are the sine identities that we have to use 

The angle here is 255, we have to use differnet angles so that we know their sine and cosine. 

255=45+210
210=180+30
This is enough to solve the problem, you need to use algebra now and search for the sine/cosine of 30,45,180 degree.

area of part 1:

a1=base*height/2=(8+2)*(8-2-2-1)/2=10*3/2=15 ft^2

area of part 2:

a2=length*width=(8+2)*1=10 ft2

area of part 3:

a3=length*width=8*2=16 ft2

total shaded area : a1+a2+a3=41 ft2

total area of the reactangle : a=16*8=128 ft2

total area of the nonshaded region : 128-41=87 ft2