A boat leaves a port and sails 7km on a bearing of 050 degrees. It then sails 9km on a bearing of 150 degrees. The boat then returns to port. How far is the journey home?.
please help i'm stuck on bearings!!, internal soon not sure if its relevant but obviously will need to know it anyway.
already tried
$$a^2+b^2=c^2\\
9^2+b^2=7^2\\
81+b^2=49\\
b^2=81-49\\
b^2= 32\\
b=4\sqrt2\ \ km $$
but I checked the answers in the book and it equals 10.4km
I just don't know how to get that answer.
Best Answer
An alternative approach is to use the Law of Cosines which states that $c^2 = a^2 + b^2 - 2ab\cos C$, where $a,b,c$ are the sides of any triangle and $C$ is the angle opposite side $c$. Using the information given in the problem, the triangle we sketch (below) has sides $a=7$, $b=9$ and $c$ to be found for the answer.
With a little geometry knowledge, we see that $m\angle C = 80^{\circ}$. So we get that $c^2 = 7^2+9^2-2*7*9*\cos(80^{\circ}) \approx 108.12 \Longrightarrow c \approx 10.398$