Pythagoras & trigonometry lesson

1. Pythagoras & trigonometry lesson SaRpythagoras.lgfl.net

2. Avoiding obstacles There are many small islands and rock formations off the UK coastline. These can add a level of complication when performing Search and Rescue operations. The Coastguard will need to give accurate instructions to the lifeboat crew as they leave their station.

3. Calculating distance When a lifeboat leaves the station, they need to know the direction and distance that they need to travel. Straight lines are the most accurate to follow. To keep precision, the Coastguard needs to aim to give as few turns as possible. How might you direct boat B to the target area?

4. Pythagoras’ theorem The Coastguard can use Pythagoras’ theorem to accurately work out the distances needed to travel using the latitude and longitude grid.

5. Pythagoras’ theorem The Coastguard can accurately measure the distances required by creating right angled triangles and using Pythagoras’ theorem. a2+ b2= c2 5.52+ 42= c2 46.25 = c2 6.80 = c (rounded to 2.d.p) You can then apply the same method to the other length.

6. Trigonometry Along with distance, the lifeboat crew also need to know the direction (or bearing) to travel. This can be worked out using trigonometry.

7. Trigonometry You can find the angle in a right angled triangle using trigonometry. In this example we can do the following: Angle = tan-1(4 ÷ 5.5) Angle = 36.03° (2.d.p) To find a bearing, you then need to perform some calculations. In this case, we have to subtract 36° from 090° - giving a bearing of 054°.

8. Putting it all together – quickly! After you’ve found the distances and direction, you can then relay this to the lifeboat crew. Quite often these calculations are actually made whilst teams are on a mission! Speed is important in these situations, but make sure your calculations are accurate!