1. ## Help with Vectors

I need help understanding how to solve these types of problems:

A plane is heading due north but finds the direction of travel to be N5*12'E. The planes air speed is 315mi/hr and wind is from west. Find the planes ground speed and speed of the wind?

At what speed with respect to the water should a boat head due north in order to follow a course of N5*15'E if a current is flowing due east at a rate of 10.6mph?

Thanks

2. Making a diagram of what is happening is strongly advised for both questions.

The angle in degrees is 5.2 degrees.

Using the cosine ratio, you can get the ground speed of the plane.

$\cos(5.2) = \dfrac{ground\ speed}{air\ speed}$

While using the sine ratio allows you to get the wind speed.

$\sin(5.2) = \dfrac{wind\ speed}{air\ speed}$

~~~~~~~~~~~
The same thing applies here, with the tangent ratio.

$\tan(5.25) = \dfrac{current\ speed}{boat\ actual\ speed}$

3. i have to face many problems in mathematics and i had great problem in vectors....please can anyone give me suggestions.