In triangle abc, ab=90 in, bc=80 in, and angle b measures 50°. what is the approximate perimeter of the triangle? a) 242.4 in. b) 265.3 in. c) 308.3 in. d) 324.1 in.

You need to use the Law of Cosines:
AC² = AB² + BC² - 2·AB·BC·cos(b)
       
Therefore, you get:

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 correct answer is A) 242.4 in