Question

a ship leaves a port P and travels 30 km due north. then it changes course and travels 20 kmp

Answer 1

Total distance = (30+20) km = 50 km

Answer 2

Image

Therefore, we may find the distance PR from triangle PCR (law of cosines) as,  

Where,  $y\quad =\quad 180^{o}-30^{o}\quad =\quad 150^{o}$

$PR\quad =\quad \sqrt { { 30 }^{ 2 }+{ 20 }^{ 2 }-2.30.29.\cos { 150^{o} }$

$PR\quad =\quad \sqrt{ { { 30 }^{ 2 } } +{ 20 }^{ 2 }-2\cdot 30\cdot 29\cdot \cos { 150^{o} }} \quad$

The distance P to R is 48 km .