M4.3.8 For the adult
Area of any triangle, and bearings
A walker leaves camp A and walks to B on a bearing of 065°. What bearing takes her back to A?
What this chapter teaches
The area of any triangle is half of two sides times the sine of the angle between them. A bearing is an angle measured clockwise from north, written with three figures. A two part journey becomes a triangle: the angle at the turn comes from the back bearing, and then the cosine rule and the sine rule give the distance and the new bearing.
Three questions to ask
There is no one right wording. Listen for the idea.
- Why must the angle in the area rule be the one between the two sides?
- Why do you add 180° to get a back bearing, and when do you take 360° away?
- How do you find the angle inside a journey triangle at the turn?
After the chapter, the learner can
- Find the area of a triangle as 1/2 ab sin C
- Give a direction as a three figure bearing, like 065°
- Solve a journey in two parts with bearings and the cosine rule
What they copy into their notebook
Area = half × a × b × sin C, with C between a and b. A bearing is clockwise from north, in three figures. Back bearing: add or take away 180°.