In triangle abc, ab=90 in., bc=80 in., and angle b measures 50 degrees. what is the approximate perimeter of the triangle?

We know that

the Law of Cosines established:
AC² = AB² + BC² - 2·AB·BC·cos(b)       
Therefore
AC = √(90² + 80² - 2·90·80·cos(50)     
=√5243.86     
= 72.4 in

Now you can sum up all the sides in order to find the perimeter:
AB + BC + AC = 90 + 80 + 72.4 = 242.4 in

the answer is
242.4 in

yes. there is an equation.