A ship sails on a bearing of 020° for 30 km.
1 answer:
Answer:
The ship travels approximately 10.261 meters to the East.
Step-by-step explanation:
At first we introduce a graphical description of the statement as an attachment below. Let suppose that bearing is respect to the North-direction, then the change in position in the East direction is modelled by the following Trigonometric formula:
(1)
Where:
- Distance travelled by the ship, measured in kilometers.
- Bearing angle, measured in sexagesimal degrees.
- Distance component in the east direction, measured in kilometers.
If we know that and
, then the distance in the East direction is:
The ship travels approximately 10.261 meters to the East.
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Answer:
Step-by-step explanation:
Opposite = BC ,
Adjacent = AB = x = 3 ,
Hypotenuse = AC = y = 22
<em><u>Using trigonometric ratios.</u></em>
Since we have adjacent and hypotenuse we use cosine's ratio
to find the angle.
When two straight lines intersect, the vertical opposite angles
intersect. the other two angles are also equal. Let the known angle be
x, then the other two adjacent angles are obtained subtracting twice of x
from 360 and dividing the result by 2.
Therefore, the table can by filled as follows:
Row 1:
Given <GEF = 120°
<FEM is adjacent to <GEF, thus
<MEH is vertically opposite to <GEF and thus is equal to <GEF. Thus <MEH = 120°
<HEG is vertically opposite to <FEM and thus is equal to <FEM. Thus <HEG = 60°.
Row 2:
Given <MEH = 150°
<MEH is vertically opposite to <GEF and thus is equal to <GEF. Thus <GEF = 150°
<FEM is adjacent to <GEF, thus
<HEG is vertically opposite to <FEM and thus is equal to <FEM. Thus <HEG = 30°.
Row 3:
Given that <FEM = 25°
<FEM is adjacent to <GEF, thus
<MEH is vertically opposite to <GEF and thus is equal to <GEF. Thus <GEF = 155°
<HEG is vertically opposite to <FEM and thus is equal to <FEM. Thus <HEG = 25°.
Row 4:
Given that <HEG = 45°
<HEG is adjacent to <GEF, thus
<HEG is vertically opposite to <FEM and thus is equal to <FEM. Thus <FEM = 45°
<MEH is vertically opposite to <GEF and thus is equal to <GEF. Thus <GEF = 135°.
Therefore, the table can by filled as follows:
Row 1:
Given <GEF = 120°
<FEM is adjacent to <GEF, thus
<MEH is vertically opposite to <GEF and thus is equal to <GEF. Thus <MEH = 120°
<HEG is vertically opposite to <FEM and thus is equal to <FEM. Thus <HEG = 60°.
Row 2:
Given <MEH = 150°
<MEH is vertically opposite to <GEF and thus is equal to <GEF. Thus <GEF = 150°
<FEM is adjacent to <GEF, thus
<HEG is vertically opposite to <FEM and thus is equal to <FEM. Thus <HEG = 30°.
Row 3:
Given that <FEM = 25°
<FEM is adjacent to <GEF, thus
<MEH is vertically opposite to <GEF and thus is equal to <GEF. Thus <GEF = 155°
<HEG is vertically opposite to <FEM and thus is equal to <FEM. Thus <HEG = 25°.
Row 4:
Given that <HEG = 45°
<HEG is adjacent to <GEF, thus
<HEG is vertically opposite to <FEM and thus is equal to <FEM. Thus <FEM = 45°
<MEH is vertically opposite to <GEF and thus is equal to <GEF. Thus <GEF = 135°.