# Question #83896

May 30, 2017

The object will be displaced by $5 m$ at ${36.9}^{0}$ south of east,
or $5 m$ approximately south east of its original location.

The total distance covered is $3 m + 4 m + 6 m = 13 m$

#### Explanation:

The object originally went out of its way to arrive at its destination.
If the object was a person and the $m$ was miles, he probably had to pick up gas on the way to work.

The object has a final displacement that can be calculated using the two given sides $4 m \mathmr{and} \frac{6 m}{2} = 3 m$ which we should memorize because they always will result in a $3 , 4 , 5 , r i g h t \angle \triangle$ which is shown as the $\mathrm{di} s p l a c e m e n t \triangle$ below.

A $3 , 4 , 5 , r i g h t \angle \triangle$ will have angles of ${36.9}^{0} \mathmr{and} {53.1}^{0}$ as well as the right angle as defined here:
http://www.mathopenref.com/triangle345.html