Question

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.

Answer 1

A. 242.4 in.

Explanation:

Answer 2

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