Answer:
46.57° or 0.8128 radians
Step-by-step explanation:
the smallest angle in this triangle is B, which is opposite the shortest side (12). We use the Law of Cosines to find B:
b² = a² + c² - 2(a)(c)·cos B
Here that works out to:
12² = 14² + 16² - 2(14)(16)·cos B, or
144 - 196 - 256 = -2(14)(16)·cos B, or:
-308 = -448·cos B, or:
-308
------------- = cos B = 0.6875
-448
Using the inverse cosine function to determine B, we get:
B = arccos 0.6875 = 0.8128 radians, or
0.8128 radians 180°
----------------------- · -------------- = 46.57°
1 π
