Question

A plane flies 400km west then 100km north.find it's distance and bearing from its start point.

Answer 1

Step-by-step explanation

The diagram of the journey can be seen below.

From the image, we can find the distance of the plane from its starting point using the Pythagoras theorem.

`\begin{gathered} D^2=100^2+400^2 \\ D^2=10000+160000 \\ D^2=170000 \\ D=√(170000) \\ D=412.3105 \end{gathered}`

Answer: Distance =412.3105km

To find the bearing, we will first find the angle "a"

`\begin{gathered} tana=(400)/(100) \\ a=tan^(-1)(4) \\ a=75.9637 \end{gathered}`

The bearing of the plane becomes

`b=180^0-75.9637^0=104.0363`

Answer: 104.0363 degrees