SOLUTION: I do not have any clue what to do with this problem. Here it is: Solving oblique triangles using the law of cosines. You have a triangle with 3 sides. It looks like thi

Algebra ->  Angles -> SOLUTION: I do not have any clue what to do with this problem. Here it is: Solving oblique triangles using the law of cosines. You have a triangle with 3 sides. It looks like thi      Log On


   

Question 113625: I do not have any clue what to do with this problem.
Here it is:
Solving oblique triangles using the law of cosines.
You have a triangle with 3 sides. It looks like this description: angle F is at the top, angle E is to the bottom right, and to the left of it is angle D.
between F and E it is 140. between E and D it is 156. between D and F is 96.
The question is: "Find the size of angle F in oblique triangle DEF.
I hope this is descriptive enough for you to help me because I honestly have no clue what to do. I don't understand the law of cosines and the Law of Sines either.
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
I do not have any clue what to do with this problem.
Here it is:
Solving oblique triangles using the law of cosines.
You have a triangle with 3 sides. It looks like this description: angle F is at the top, angle E is to the bottom right, and to the left of it is angle D.
between F and E it is 140. between E and D it is 156. between D and F is 96.
The question is: "Find the size of angle F in oblique triangle DEF.
I hope this is descriptive enough for you to help me because I honestly have no clue what to do. I don't understand the law of cosines and the Law of Sines either.



The law of cosines for when you have all three sides and
no angle given is

                 (one ADJACENT side)² + (other ADJACENT side)² - (OPPOSITE)²
cosine(ANGLE) = -------------------------------------------------------------
                      2(one ADJACENT side)(other ADJACENT side)


The ANGLE we want to find is F.
One ADJACENT side to F is DF which is 96 in length.
The other ADJACENT side is EF which is 140 in length.
The OPPOSITE side is the side across the triangle
from angle F, which is DE, 156 in length.

cos%28F%29=%2896%5E2%2B140%5E2-156%5E2%29%2F%282%2A96%2A140%29 

cos%28F%29=%289216%2B19600-24336%29%2F%2826880%29

cos%28F%29=%284480%29%2F%2826880%29

cos%28F%29=.1666666667%29

Now we find the inverse cosine of that
and we get 

Angle F = 80.40594177°

Since the sides given are rounded to
3 significant digits, we round the
angle off to the nearest degree, so
the answer is 

Angle F = 80°

Edwin