Question

Suppose you first walk 12.0 m in a direction 200 west of north and then 20.0 m in a direction 40.00 south of west. How far are you from your starting point, and what is the compass direction of a line connecting your starting point to your final position?

Answer 1

Complete Question

The  complete question is shown on the first uploaded image

Answer:

the compass direction of the resultant displacement is  $\theta =4.7^o$ south of west

Explanation:

Generally using cosine we can obtain the resultant R as follows

     $R^2 = A^2 + B^2 -2ABcos(70)$

=>   $R = \sqrt{12^2 + 20^2 - 2(12 ) * (20) cos 70}$

=>    $R = 19.48 \ m$

We can obtain the direction of the resultant by first  using sine rule to obtain angle C as follows

       $\frac{A}{sin C} = \frac{R}{sin70 }$

=>    $C= sin ^{-1} [\frac{A * (sin 70)}{R} ]$

=>    $C = sin ^{-1} [\frac{20 * (sin 70)}{19.48} ]$

=>  $C = 74.7 ^o$

Then the direction is obtained as

       $\theta = C - 70$

=>    $\theta = 74.7 - 70$

=>     $\theta =4.7^o$

Hence the compass direction of the resultant displacement is  $\theta =4.7^o$ south of west