Question

A treasure map required that the seekers, starting from a certain point X, walk 10 m due North, then 17 m due East followed by 25 m due South. Determine the magnitude and the direction of the treasure seekers starting point.

Answer 1

Gives

Certain point (X)

North direction(AE)= 10 m

East(BC)=17 m

South(CE)=25 m

North to South total distance

Path

DE=CE-AB=25-10=15m

West to east distance =17m

Resultant(AE)= $\sqrt{AD^2+DE^2}$

$$AE=\sqrt{17^2+15^2}=\sqrt{514}=22.67m$$

Magnitude of direction

AE =22.67m

Resultant direction South -east direction

Where angle $i=\theta$

$tan\theta =\frac{15}{17}$

$\theta=tan^{-1}\frac{15}{17}$

$\theta=41.42°$

Resultant direction South-east

positive x-axis make angle is41.42°