Complete Question
The complete question is shown on the first uploaded image
Answer:
the compass direction of the resultant displacement is [tex]\theta =4.7^o [/tex] south of west
Explanation:
Generally using cosine we can obtain the resultant R as follows
[tex]R^2 = A^2 + B^2 -2ABcos(70)[/tex]
=> [tex]R = \sqrt{12^2 + 20^2 - 2(12 ) * (20) cos 70}[/tex]
=> [tex]R = 19.48 \ m[/tex]
We can obtain the direction of the resultant by first using sine rule to obtain angle C as follows
[tex]\frac{A}{sin C} = \frac{R}{sin70 }[/tex]
=> [tex]C= sin ^{-1} [\frac{A * (sin 70)}{R} ][/tex]
=> [tex]C = sin ^{-1} [\frac{20 * (sin 70)}{19.48} ][/tex]
=> [tex]C = 74.7 ^o[/tex]
Then the direction is obtained as
[tex]\theta = C - 70[/tex]
=> [tex]\theta = 74.7 - 70[/tex]
=> [tex]\theta =4.7^o [/tex]
Hence the compass direction of the resultant displacement is [tex]\theta =4.7^o [/tex] south of west
