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# HELP ME!!

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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)

May 12, 2021
edited by ughh.abby  May 12, 2021

#1
+120287
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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

May 12, 2021
#2
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D  =   ( 14.2 sin ) (41.66 ) / sin 9.68   ≈  56.1  mi

May 12, 2021