Question

An aeroplane leaving from Bismarck travels on a bearing of ${120}^o$, as shown in the figure. If the plane is $295$ miles directly east of Pierre, how far apart are Bismarck and Pierre? select your answer to the nearest mile.

• A. $170$
• B. $160$
• C. $150$
• D. $140$

Answer 1

The correct option is A $170$

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

So, $\tan \left({60}^o\right)=\frac{295}{x}$

where, $x$ is the distance between Bismarck and Pierre.

$\therefore x=\frac{295}{\sqrt{3}}=170.31$ miles, the nearest integer being $170$ miles