# Course and Ground Speed (Navigation problem)

#### Elidibz

1. The problem statement, all variables and given/known data

A plane flies in the direction 120 degrees with an air speed of 300mph. The wind is blowing north to south at 40mph. Find the course and ground speed of the plane.

2. Relevant equations

3. The attempt at a solution

I attempted this problem, but i still cannot figure out how we get the second angle?

#### Mark44

Mentor
Have you drawn a picture?
Do you know how to decompose vectors into their components? If you don't know how to work with vectors, your picture should help you get the largest angle in the triangle formed by the plane's direction vector and the wind's vector. You know two of the sides of the triangle and the angle between them, so you can use the law of cosines to find the third side of the triangle. After you have found it, you can use the law of sines to find one of the remaining angles in the triangle.

#### chaoticflow

Draw the vectors as suggested. The final velocity of the airplane is the sum of the two vectors.

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