SOLUTION: Hi a ship travels 45 km in a direction with a bearing of 132 degrees. How far south of its starting point is the ship. thanks

Question 1091632: Hi
a ship travels 45 km in a direction with a bearing of 132 degrees. How far south of its starting point
is the ship.
thanks
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
a bearing of 132 degrees is an angle that is clockwise from north.
that would be angle NAB in the picture.

AB is the distance the ship travels along that direction.

BC is the line formed by extending a horizontal line from B to the north south line of NC.

48 degrees is angle CAB which is the supplement to angle NAB.

the triangle formed is ABC.

angle BAC is 48 degrees.
angle BCA is 90 degrees.
angle ABC is complement to BAC = 90 - 48 = 42 degrees.

the line AC is how far south the ship is.
the line AB is the distance the ship traveled and also the hypotenuse of right triangle ACB.

cos(48) = AC / AB.
AC = AB * cos(BAC) = 45 * cos(48) = 30.11 rounded to 2 decimal place.

sin((ABC) = AC / AB.
AC = AB * sin(ABC) = 45 * sin(42) = 30.11 rounded to 2 decimal places.

either way you get AC= 30.11 kilometers.

$$$

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