Applied Math- Cosine law

Question

Applied math- Cosine law 

Alex, Curtis and Michael go boating together on a calm day. They leave the marina dock and travel at a speed of 40 km/h due east for 3 hours. Then, they travel 22° west of south for 2 hours at a speed of 30 km/h. At that point, their boat breaks down and they call the mechanic at the marina dock to come and help them.

To get to them in the shortest time, how far must the mechanic travel and in what direction?

1. 1 mark for an appropriate diagram
2. 1 mark for finding the enclosed angle
3. 1 mark for setting cosine law up properly
4. 1 mark for finding the distances the boats travel
5. 1 mark for finding the measure of angle A
6. 1 mark for giving a correct direction

Answer 1

From the starting point to the break-down the length is (a^2+c^2-2ac*cosβ)^.5=b

(60^2+120^2-14,400*cos68)^.5=112.274km

angle: α=acos((b^2+c^2-a^2)/(2bc))=acos((112.275^2+120^2-60^2)/(26,946)=29.7°ese