Aircraft bearing

Two aircraft will depart from the airport simultaneously. The first flight flies with a course of 30°, and the second with a course of 86°. Both fly at 330 km/h. How far apart will they be in 45 minutes of flight?

Correct answer:

x =  232.3884 km

Step-by-step explanation:

$$\begin{gathered} v=330\text{km/h} \\ t=45\text{min}\to \text{h}=45:60\text{h}=0.75\text{h} \\ a=v\cdot t=330\cdot 0.75=\frac{495}{2}=247.5\text{km} \\ b=a=247.5=\frac{495}{2}=247.5\text{km} \\ \alpha =86-30=56{}^{\circ } \\ {x}^2=a^2+b^2-2\cdot a\cdot b\cdot \cos \alpha \\ x=\sqrt{a^2+b^2-2\cdot a\cdot b\cdot \cos \alpha }=\sqrt{a^2+b^2-2\cdot a\cdot b\cdot \cos 56°}=\sqrt{247.5^2+247.5^2-2\cdot 247.5\cdot 247.5\cdot \cos 56°}=\sqrt{247.5^2+247.5^2-2\cdot 247.5\cdot 247.5\cdot 0.559193}=232.388=232.3884\text{km} \end{gathered}$$

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