Question

20. A ship travels 6km south, and then 8km west. Draw a diagram of the situation and then determine the resulting direction (as a bearing) that the ship traveled from source to destination, correct to the nearest degree.

Answer 1

A ship travels 6km south, and then 8km west.

The diagrammtic expression is shown below

To find θ, we will apply SOHCATOA

Given

`\begin{gathered} Opposite=8\text{ km} \\ Adjacent=6\text{ km} \end{gathered}`

Applying the tan formula

`\tan\theta=(Adjacent)/(Hypotenuse)`

Substitute the values of the side lengths into the formula above

`\begin{gathered} \tan\theta=(8)/(6) \\ \tan\theta=1.3333 \\ \theta=\tan^(-1)(1.3333) \\ \theta=53.13\degree \end{gathered}`

The bearing of the ship from the source to destination will be

`\begin{gathered} =\theta+180\degree \\ =53.13+180\degree=233.13\degree \\ =233\degree\text{ \lparen nearest degree\rparen} \end{gathered}`

Hence, the answer is 233° (nearest degree)