Trigonometry Fun with Military Desert Tanks!

How far must a military desert tank travel to be due east of point a?

The military desert tank manoeuvres 13.5 km from point a on a bearing of 042° to point b. From point b, how far due south must the tank travel to be at a point due east of point a?

Answer:

The military desert tank needs to travel approximately 10.2 km due south from point b to be due east of point a, using trigonometry in a right-angled triangle created by the tank's path.

Trigonometry can be a fun way to solve real-world problems, like maneuvering military desert tanks! In this scenario, the tank travels 13.5 km from point a to point b on a bearing of 042°.

We first need to determine the angle in standard position corresponding to the bearing of 042°. By subtracting 042° from 90°, we find that the angle is 48°. This angle will be crucial in our trigonometric calculations.

Using the sine function, sin(48°) = opposite/13.5 km, we can calculate the distance the tank must travel due south from point b to be due east of point a. Solving for the opposite side, we find that the tank needs to travel approximately 10.2 km due south.

Trigonometry allows us to analyze and solve various navigation and distance problems, making it a valuable tool in mathematics and real-life applications. So next time you see a military desert tank on the move, remember the trigonometric calculations involved!