# Solve the following problem using analytical techniques: Suppose you walk 17.5 m straight west and then 24.0 m straight north. How far r you from your starting point, & what is the compass direction of a line connecting your starting point to your final?

## (If you represent the two legs of the walk as vector displacements A and B, as in the figure below, then this problem asks you to find their sum R = A + B. Give the direction in degrees north of west.)

Jul 18, 2017

Simply calculate your hypotenuse and angle

#### Explanation:

You first went to West and North.

Your hypotenuse is your total distance from the starting point:

${R}^{2} = {A}^{2} + {B}^{2}$

${R}^{2} = {17.5}^{2} + {24}^{2}$

${R}^{2} = 306.25 + 576$

$R = \sqrt{882.25} = 29.7$ meters

However it is not a right statement that $R = A + B$ (The statement provided on the figüre is WRONG!).

Your direction is northwest.

Now use trigonometry:

$\sin \theta = \frac{B}{R}$

$\sin \theta = \frac{24}{29.70} = 0.808$

$\theta = 53.9$ degrees. This is your angle.