An aeroplane flies due north from airport P to Q and then flies due east R. If Q is equidistant from P and R, find the bearing of P and R
A. 90o
B. 135o
C. 225o
D. 270o
The bearing is the angle measured clockwise from the north direction.
Since the airplane flies due north from P to Q, the bearing of P is 0 degrees.
Since Q is equidistant from P and R, the triangle PQR is an isosceles right triangle.
Therefore, the bearing of R is 90 degrees more than the bearing of Q.
Since the airplane flies due east from Q to R, the bearing of R is 90 degrees.
Thus, the bearing of P is 0 degrees and the bearing of R is 90 degrees.
Therefore, the correct answer is D. 270o.
To find the bearing of point P and R, we need to consider the direction of the flight from P to Q (north) and then the direction from Q to R (east).
Since the airplane is flying due north from P to Q, the bearing of Q from P is 0 degrees. This is because 0 degrees represents the direction directly north.
Then, since Q is equidistant from P and R, the airplane must have flown in a straight line from Q to R. Since it is flying due east, the bearing of R from Q is 90 degrees. This is because 90 degrees represents the direction directly east.
To find the overall bearing of R from P, we add the two bearings together:
0 degrees (bearing of Q from P) + 90 degrees (bearing of R from Q) = 90 degrees.
Therefore, the bearing of P and R is 90 degrees, which corresponds to option A.