a plane is seen to travel in a direction [S30 degreesW]. If its ground velocity was 300 km/h and the wind speed is 150 km/h south, what is the plane's velocity relative to the air?
Let denote the vector $\displaystyle \overrightarrow{OW}$ the plane's velocity and direction through the air, the vector $\displaystyle \overrightarrow{OP}$ the plane's velocity and course over ground and $\displaystyle \overrightarrow{OS}$ the velocity and direction of the wind.
Then $\displaystyle |\overrightarrow{OW} | = |\overrightarrow{PS}|$
Use Cosine rule to calculate the length of $\displaystyle \overline{PS}$
I've got $\displaystyle |\overrightarrow{OW} |= |\overrightarrow{PS} | \approx 185.897\ \frac{km}{h}$