Question

A person walks 33 m East and then walks 38 m at an angle of 35 degrees North of East. What is the magnitude of the total dis-placement ? Answer in units of m.

Answer 1

Let's assume that person starts at point A, after walking 33m East he/she changes the direction at point B and then stops walking and point C. We have triangular ABC with AB=33m, BC=38m, $\angle B= 35^\circ$ .The total displacement is the side of triangular AC. To find it we can use cosine theorem:

$AC^2 = AB^2 + BC^2 - 2 AB \cdot BC \cdot cos35^\circ$

$AC^2 = 2533- 2054=479$

$AC = \sqrt{479}=21.9 \approx 22$ m.

Answer: 22 m.