a man sails 30 km from a port to a lighthouse Q on a bearing of 128 then he sails another 25 km to R on a bearing of 295 calculate the distance of pr

Respuesta :

let's say that the boat leaves the port at (0,0) coordinates
the x axis is W-E
and they axis is S-N

he will go first 30 clicks to ESE at an 128 angle from the north direction
that means he will go 30*cos128 clicks to south and 30*sin128 clicks to east
then he will go 25*cos295 clicks to north and 25*sin295 clicks to west

the coordinates of the point R are
x=30*sin128+25*sin295 = 30*0.788+25*(-0.906) = 23.640-22.657=0.983
y=30*cos128+25*cos295 =30*(-0.615)+25*0.422= -18.450+10.565= -7.885

apply pitagora for those and you'll have the PR distance
PR^2= 0.983^2+7.885^2=0.966+62.173 = aprox 64
that means PR is almost 8 clicks