Hello, BiGpO6790!

A car is driven east for a distance of 45 km, then north for 29 km,

and then in a direction 29° east of north for 27 km.

Determine:

(a) the magnitude (in km) of the car's total displacement from its starting point

(b) the angle (from east) of the car's total displacement measured from its starting direction. Code:

N * D
: /:
:29°/ :
: /27: y
: / :
:/61° :
C * - - * E
| x :
| :
29 | : 29
| :
A * - - - - - - * - - *
45 B x F

The car started at , drove east 45 km to ,

then north 29 km to , then at heading N29°E for 27 km to

We have: .

. .

Let

Draw line segment

Its length is the displacement in part (a).

. . In right triangle .[1]

In right triangle

Substitute into [1]: / .(a)

We want: .

Therefore: . .(b)