Point P and Q are respectively 24km North and 7km east of point R , what is the bearing of P and Q?
Assuming you mean the bearing from point R,
P is due north
Q is due east
All angles are measured CW from the +y-axis.
P = 0o.
Q = 90o.
To determine the bearing of points P and Q from point R, we need to use trigonometry. Bearing is the angular direction measured clockwise from a reference point, usually North. Here are the steps to calculate the bearings:
Step 1: Draw a diagram
Start by drawing point R at the origin of a coordinate system. Draw two lines, one 24 km long towards the North, and another 7 km long towards the East. Label the endpoint of the North line as point P, and the endpoint of the East line as point Q.
Step 2: Calculate the angle between the North line and the reference line
Using trigonometry, we can find the angle between the North line and the reference line (usually North). The opposite side (24 km) represents the distance North and the adjacent side (0 km) represents the distance East. The tangent of the angle can be calculated as:
tan(θ) = opposite/adjacent
tan(θ) = 24/0 (division by zero is undefined)
Since the adjacent side is 0 km, we can conclude that the angle is 90 degrees (or 270 degrees if measured clockwise).
Step 3: Calculate the angle between the East line and the reference line
Next, we need to calculate the angle between the East line and the reference line (usually North). The opposite side (7 km) represents the distance East and the adjacent side (0 km) represents the distance North. The tangent of the angle can be calculated as:
tan(θ) = opposite/adjacent
tan(θ) = 7/0 (division by zero is undefined)
Again, since the adjacent side is 0 km, we conclude that the angle is 90 degrees (or 270 degrees if measured clockwise).
Step 4: Determine the final bearing
To get the final bearing of points P and Q, we need to consider the reference point (usually North). Since the North line has an angle of 90 degrees (or 270 degrees) with reference to North, the bearing of point P from point R is 90 degrees (or 270 degrees) clockwise from North. Similarly, since the East line also has an angle of 90 degrees (or 270 degrees) with reference to North, the bearing of point Q from point R is also 90 degrees (or 270 degrees) clockwise from North.
In conclusion, the bearing of point P and Q from point R is 90 degrees (or 270 degrees) clockwise from North.