Battleship Trigonometry.

Apologies for not publishing anything yesterday but the internet has been extremely slow for the past few days.  When I tried to write this column, the internet basically stalled so bad, I couldn't even download my mail.  It looks like I'm back again.

I just got the latest issue of The Mathematics Teacher from the National Council of Teachers of Mathematics and on the front was an article on this topic.

I'd never thought of using trigonometry in reference to battleships.  The article starts with an explanation of armors and ships.  Since I know nothing about battleships, the explanation of "belt armor"(vertical plane or side) and "deck armor" (horizontal plane or top of the ship).  This is needed as the author goes on to show how an artillery shell might hit the belt armor or deck armor.

For purposes of the exercise, most factors affecting the shells ability to penetrate the armor is ignored and the penetration is set at 400 mm or the thickness of armor that a shell can pass through and cause damage.  In other words, if the armor is thick enough, the shell will not cause any damage, if not, the armor is damaged.

The idea behind the exercise is to use the path of the shell passing through the armor as the hypotenuse of a right triangle while the inner wall of the armor is the side and if a line is drawn between the shell's path and the inner wall, you get the other side.  Then just after the drawings are shared and before the math is done, students are encouraged to make predictions of will the shell penetrate either armor.

The second part is taking various values for range or distance from target, angle of depression, and artillery penetration (values taken from real life facts from the Iowa class battleships for the United States Navy 16 inch Mark 7 guns.  They use this information plus the definition of the sin ratio to determine the thickness of the armor and if the shell will penetrate the ship.  This math is similar to the math done by those who design battleships.

At the end, students should discover that the belt armor is more vulnerable than the deck armor even though it is thicker.  I didn't know this application of trig and since I've just started teaching trig ratios in my Algebra II class, I plan to use this activity early next class with those students.  I think its important to show students real life applications that do not seem contrived.

Please check it out for more details but I'm thrilled with this application and I'll report back with the results later next week, hoping the internet does not go down again.  Let me know what you think, I'd love to hear.  Have a great day.