To calculate (approximate) the distance between the enemies, calculate first the distance between the army post to the enemies.

The distance between the post and enemy 1 can be approximated by using the speed of sound and the time interval between the flash and the report. Thus, \(d_1 = \frac{1140 ~ft}{sec} (5 ~sec) = 5700 ~ft\)

Same with enemy 2, \(d_2 = \frac{1140 ~ft}{~sec} (4) = 4560 ~ft\)

Calculate the distance between them.

\(y^2 = 5700^2 + 4560^2 - 2 (4560)(5700) \cos 40\)

The two enemies are probably \(y = 3669 ~ft\) apart. Answer

Will you be doing trigonometry in the heat of a fight?