Looks like if you set up this triangle it will look something like so:
E_______________F
\ /
\ /
\ / 4.3
2.7 \ /
\ 120 /
\ /
\ /
D
I can't draw the triangle to scale clearly, but at least the angle and sides are correctly labeled.
Since you know two sides and the angle in between those sides, the law of cosines is the appropriate line of attack for this problem. For the sake of the problem, I will refer to side EF as c, side DE as a, and side DF as b. Then with the law of cosines:
c2 = a2 + b2 - 2abCos(C)
Substituting in our values:
c2 = 2.72 + 4.32 - 2(2.7)(4.3)Cos(120)
Simplifying the right side we should end up with:
c2 = 37.39
Solving for c:
c = 6.1147
Thus, the missing side of the triangle EF = 6.1147 meters.
To find angle DEF now we will use law of sines. Here, DEF we will refer to as angle B and then:
sin(120)/6.1147 = sin(B)/4.3
Multiply both sides by 4.3 and we end up with:
.609 = sin(B)
Finally we can use inverse sine to solve for B.
B = 37.5 degrees. Which means our angle DEF is 37.5 degrees, and for good measure, we can conclude that the final missing angle, DFE is 22.5 degrees since all the angles must add to 180 degrees.
Hope this helps!
