Point x is 5km from y on a bearing of 070 degree calculate how much further north x is than y
5 km
To find out how much further north point x is than y, we first need to determine the north component of the distance between the two points.
The bearing of 070 degrees indicates an eastward direction. To calculate the north component, we need to find the sine of the angle formed between the line connecting x and y and the north direction.
The angle formed is the complement of the bearing angle, which is 90° - 70° = 20°.
Next, we calculate the north component using trigonometry:
North component = Distance between x and y * sin(angle)
Given that the distance between x and y is 5 km, the calculation will be:
North component = 5 km * sin(20°)
Calculating this, we find:
North component = 5 km * 0.3420
North component ≈ 1.71 km
Therefore, point x is approximately 1.71 km further north than point y.
To calculate how much further north point x is from point y, we need to find the component of the distance between x and y that is in the north direction.
First, let's convert the bearing from degrees to radians. We can do this by multiplying the bearing by π/180.
Bearing in radians = 070 * π/180
Next, we can use trigonometry to find the vertical (north) component of the distance between x and y. We know that the sine of an angle is equal to the opposite side divided by the hypotenuse. In this case, the opposite side is the north component of the distance, and the hypotenuse is the total distance (5km).
North component = 5km * sin(bearing in radians)
Finally, we have the north component, which represents how much further north x is than y. This value gives us the answer to your question.