Question

An aeroplane leaving from Bismarck travels on a bearing of ${120}^o$, as shown in the figure. If the plane flew at an average rate of $400$ miles per hour, how many minutes (approx) had it been in the air when it was $295$ miles from Pierre?

• A. $51$
• B. $56$
• C. $29$
• D. $67$

Answer 1

The correct option is A $51$

The angle that the plane makes with the line joining Bismarck and Pierre is ${60}^o$

We thus have $\sin \left({60}^o\right)=\frac{295}{x}$ where $x$ is the distance flown by the plane.

That distance becomes $x=\frac{295\times 2}{\sqrt{3}}$

$x=340.63$ mi

Since the speed is $400$ miles per hour, the time becomes $340.63/400\times 60=51.0945$ minutes