Three towns p, q and r are such that the distance between p and r is 90km. If the bearing of q from p is 075 and the bearing of r from p is 310, find the
(a)distance between q and r
(b)bearing of r from q
You know one angle, angle P, and one side, q (PR). I don't see that it can be solved. Something is missing, I suspect the distance pq (Side r).
from a ship p, the bearing of a harbour Q is 070 degrees.
To find the distance between q and r, we can use the concept of bearings and the given information about the distances between towns.
(a) Distance between q and r:
From the given information, we have the bearing of q from p as 075, which means that the angle between the line connecting p and q and the north line is 75 degrees. Similarly, the bearing of r from p is 310, implying that the angle between the line connecting p and r and the north line is 310 degrees.
To determine the distance between q and r, we need to find the third side of the triangle formed by the three towns. We can use the Law of Cosines to solve for this third side.
Using the Law of Cosines, the formula for finding a side of a triangle is:
c² = a² + b² - 2ab * cos(C)
Here, a and b represent the lengths of the two known sides, and C is the angle opposite to the unknown side.
Let's calculate the distance between q and r:
c² = 90² + 90² - 2 * 90 * 90 * cos(310 - 75)
c² = 8100 + 8100 - 16200 * cos(235)
c² = 16200 - 16200 * cos(235)
c² = 16200 - 16200 * (-0.3420)
c² = 16200 + 5547.6
c² ≈ 21747.6
c ≈ √21747.6 ≈ 147.48 km
Therefore, the distance between q and r is approximately 147.48 km.
(b) Bearing of r from q:
The bearing of r from q can be found by subtracting the bearing of q from p from the bearing of r from p.
Angle between q and r = bearing of r from p - bearing of q from p
Angle between q and r = 310 - 75
Angle between q and r = 235 degrees
Hence, the bearing of r from q is 235 degrees.