A point p is 40km from the q on a bearing 061 calculate the distance that p is
@ north of q
B east of q
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61 degrees clockwise from north looking from q to p
so
North distance = 40 cos 61 = 19.4 km
Easst distance = 40 sin 61 = 35.0 km
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To calculate the distance between point P and point Q in different directions, we can use trigonometry. Here's how to calculate the distances:
1. Distance north of Q: Since the bearing is 061, it means the direction is slightly east of north. We can use the cosine and sine functions to find the distances in the north and east directions.
To find the distance north of Q, we'll use the cosine function. The formula is:
Distance north = distance * cos(angle)
In this case, the distance is 40 km and the angle is 29 degrees (061 degrees - 90 degrees = -29 degrees because the angle is measured clockwise from north).
Distance north = 40 km * cos(-29 degrees)
Distance north = 40 km * 0.866 (cosine of -29 degrees)
Distance north = 34.64 km (rounded to two decimal places)
So, point P is approximately 34.64 km north of point Q.
2. Distance east of Q: Since the bearing is 061, it means the direction is slightly east of north. We can use the cosine and sine functions to find the distances in the north and east directions.
To find the distance east of Q, we'll use the sine function. The formula is:
Distance east = distance * sin(angle)
In this case, the distance is 40 km and the angle is 29 degrees (same as before).
Distance east = 40 km * sin(29 degrees)
Distance east = 40 km * 0.5 (sine of 29 degrees)
Distance east = 20 km
So, point P is 20 km east of point Q.
Therefore, the distances are:
- Point P is approximately 34.64 km north of point Q.
- Point P is 20 km east of point Q.