A ship is sailing east. At one point, the bearing of a submerged rock is
48°20′. After the ship has sailed 14.2 mi, the bearing of the rock has become
308°40′. Find the distance of the ship from the rock at the later point.
The distance is ___ mi.
(DO NOT ROUND UNTIL THE FINAL ANSWER. THEN ROUND TO THE NEAREST TENTH AS NEEDED)
We can form a triangle with two known a known base and two known base angles
We need to convert bearing to "regular" angles
The first base angle = 90 - 48° 20 min = 41° 40 min = 41.66°
The second base angle = 308° 40 min - 270 = 38° 40min= 38.66°
The other angle of the triangle = 90 - 41.66 - 38.66 = 9.68°
We can use the Law of Sines to find the distance from the ship to the rock = D
14. 2 / sin 9.68 = D / sin 41.66
D = ( 14.2 sin ) (41.66 ) / sin 9.68 ≈ 56.1 mi