Question

A ship is sailing east. at one​ point, the bearing of a submerged rock is 44 degrees 20 prime44°20′. after the ship has sailed 15.715.7 ​mi, the bearing of the rock has become 308 degrees 40 prime308°40′. find the distance of the ship from the rock at the latter point.

Answer 1

Let A be the position of the ship at which the rock is found at B, after travelling 15.7 miles the ship reaches point C, thus ABC forms a triangle that has the dimensions of
AC=15.7
and
∠x=BAC=90-44°20'=45°40'
∠y=∠BCA=360-270=90
∠ABC=180-∠x-∠y=44°20'
therefore using sine law
BC/sin (44°40')=15.7/sin (45°20')
⇒BC=15.5184 miles