finding distance and bearing of a yacht

hi,

can someone please help me with this? can it be solved with vectors?

*A yacht sails 7 km on a bearing 064° followed by 16 km on a bearing 038°. *

Calculate the distance (in km to the nearest 0.1 km) and bearing (to the nearest degree) of the yacht's final position from its initial position.

thanks!

Re: finding distance and bearing of a yacht

Have you made a design already? ...

Re: finding distance and bearing of a yacht

There are two ways to handle vector problems like this:

1) Find the "x and y" components of each vector: if a vector has length r at angle $\displaystyle \theta$ to the positive x-axis (which you can take to be "East") then its x component is $\displaystyle r cos(\theta)$ and its y component is $\displaystyle r sin(\theta)$. After finding components, you can add the vectors by adding the individual components. Finally use the Pythagorean formula to find the total distance.

2) Drawing the two legs of the voyage and then connecting the beginning and end points gives you a triangle. You know the length of the two legs and can find the angle where the two legs join: if the two given bearings are [tex]\theta1[tex] and $\displaystyle \theta2$, then the angle in the triangle is $\displaystyle 180- (\theta2- \theta1)$. Use the "cosine law", $\displaystyle c^2= a^2+ b^2- 2ab cos(C)$, to find the length of the third side.