Question

A man wandering in the desert walks 2.7 miles in the direction S 35°W. He then turns 90° and walks 3.5 miles in the direction N 55° W. At that time, how far is he from his starting point, and what is his bearing from his starting point?

Answer 1

To solve this problem we will make a diagram in the Cartesian plane that will allow us to find and understand more accurately the displacement and the angle of rotation.

According to Pythagoras, the distance traveled would be equivalent to

`d = √((2.7)^2+(3.5)^2)`

`d = 4.4 miles`

The individual had a displacement of 4.4 thousand from the starting point.

Now the angle
`\theta` plus the previously given angle will allow us to find the direction of travel.

`tan\theta = \frac{\text{Opposite side}}{\text{Adjacent side}}`

`tan\theta = (3.5)/(2.7)`

`\theta = tan^(-1) ((3.5)/(2.7))`

`\theta = 52.35\°`

`\angle =`
`\theta + 35 = 52.35+35 = 87.35\°`

Therefore the net direction of the man is S 87.35° W