Question 1057675
We use the SAS formula. SAS stands for Side-Angle-Side:
c^2 = a^2+b^2-2ab cos(C)
where we have three sides, a, b, c, and c is our unknown side. C is the angle we know, it's opposite side c. Plug in the numbers:
c^2 = [(7^2+4^2)-2*7*4*cos(53)
c^2 = 49+16-56*0.602 = 31.288
sqrtc^2 = sqrt31.288
c = 6 
There is only one triangle with sides 4, 6, 7 and angle C = 53°
:
John