Solving a triangle means identifying length of all the three sides as well as measures of all three angles. This is generally done using Law of sines, which is a/sinA=b/sinB=c/sinC and Law of cosines, according to which b^2=a^2+c^2-2ac cosB, c^2=a^2+b^2-2abcosC and a^2=b^2+c^2-2bc cosA. Here three sides of triangle are a, b and c and angles opposite to them are A, B and C.
Here, we are given DeltaFGH and g=14, /_G=80^o and H=40^o. It is apparent that /_F=180^o-80^o-40^o=60^o#
We can use sine formula to get side h. Using ^^Law of sines**
f/(sin60^o)=14/(sin80^o)=h/(sin40^o) and hence
h=14/(sin80^o) xx sin40^o=14/0.9848xx0.6428=9.1381
and f=14/(sin80^o)xxsin60^o=14/0.9848xx0.866=12.311
Hence, triangle is f=12.311, g=14, h=9.1381, F=60^o, G=80^o and H=40^o.
