# solving word problems of triangles/bearings

This is a long word problem so be prepared.

A group of computer game junkies decided to act out their sky rim adventures in real-life. Till Whompson, Mampton Cunninghah, Baaron Bew, Mas Darnol, and Whephan Stidener all set out from Mas Darnol's house on a bearing of N 62 degrees E for 3 miles. After stopping at the local restaurant called the Boar's Nest for some grub, they decided to head on a new bearing of S 25 degrees W for 5 miles. Unfortunately, they were ambushed by the deadly water bubble monsters. Mampton immediately was devoured by one of the monsters, and Till, Baaron, and Wephan all knocked themselves out when they turned to run away. Fortunately Mas escaped and headed back home. What bearing should Mas take to get back to his house and how far will he have to travel?

I already calculated how far he will have to travel and got $3.32$ miles using law of cosines. This could be wrong, and if it is feel free to correct me but what I am having so much trouble with is the bearing. I cannot figure it out for the life of me. Please help!

Here's a nice diagram.

Using the Law of Cosines:

\begin{align} c^2&=a^2+b^2-2ab\cos C\\ c^2&=3^2+5^2-2\cdot3\cdot5\cos37\\ c^2&=34-30\cos37\\ c&=\sqrt{34-30\cos37}\\ c&\approx3.16874 \end{align}

$\theta$ can be found with the Law of Sines:

\begin{align} \sin\theta&\approx\frac{\sin37}{3.16874}\cdot3\\ \sin\theta&\approx0.56977\\ \theta&\approx34.73 \end{align}

The direction is North $(34.73-25)$ degrees West

• Thank you very much for your help! – Ila Isabelle Apr 27 '14 at 23:37

Two ships left the same port; one going in the direction N 70 E and the other is sailing directly East. The first ship traveled at the rates of 15 mph. After 30 minutes, the second ship was observed to be directly South of the first. What is the speed per hour of the second ship?