Question

A man walked 50 m to the south, turned, walked 40 m to the west.
4. Which direction best describes his final position?
A. 649
B. 231°
C. 2929
D. 331°

Answer 1

Answer:

Direction is N 51.3° E

Explanation:

» From trigonometric ratios:

${ \tt{ \red{ \tan( \theta) = \frac{opposite \: { \blue{(south)}}}{adjacent \: { \blue{(west)}}} }}} \\ \\ { \tt{ \tan( \theta) = \frac{50}{40} = \frac{5}{4} }} \\ \\ { \tt{ \theta = { \tan }^{ - 1} ( \frac{5}{4}) }} \\ \\ { \tt{ \theta = 51.3 \degree}} \\ \\ { \boxed{ \tt{ \: direction : \:{ \green{N }}\: 51.3 \degree \: { \green{ E }}}}}$