Question

An aeroplane travels 40 km on a bearing of 060° and then another travels 60 km on a bearing of 100°
(a) Draw the scale drawing choosing a suitable scale.
(b) How far is the aeroplane from the starting point?
(c) Find the bearing of the last destination from the starting point.


answer all 3(a, b, c) ​

Answer 1

Answer:

Let’s call the starting point A, the second point after 300km B and the third point C. The angle at points A, B and C, will be called a, b and c, respectively.

If we draw the diagram, we can see that the point form a triangle ABC, and we know:

AB = 300

BC = 400

c = 130 degrees

First we can use the Cosine rule to find the length AC.

AC^2 = 400^2 + 300^2 + 2*400*300*cos(130)

AC^2 = 95730.9736…

AC = 309.404 (3dp)

Now that we have AC we can use sine rule to find the size of angle c.

sin(c) = sin(130) * 300/309.404

c = sin-1(sin(130) * 300/309.404)

c = 47.96 degrees (2dp)

The bearing from the final direction is a clockwise turn until we are 47.96 degrees from the line BC. So:

180 - 47.96

= 132.04 degrees is the final bearing.