a traveler moves from a town p on a bearing of 055degree to another town q 200 km away, he then moves from q on a bearing of 155degree to another town r 400km from q.find the distance between p and r,bearing of p from r correct to 3significant figures (mathematics:topic is bearing and distance)
A travelled move from a town p on a bearing of 55toQ200kmaway then proves from Q in a bearing of 155 to a town R400km find(a)distance b/w p and R (b)bearing ofP from Q
A Traveller moves from a town p on a bearing of 055'0 to a town q 200km away.he then moved from q.find the distance between p and r,bearing of p from Court to the nearest degree
330.17°
To find the distance between town P and town R, we need to break down the problem into two parts: finding the coordinates of each town and then calculating the distance between them using the distance formula.
Step 1: Find the coordinates of town P.
Since the traveler moves from town P on a bearing of 055 degrees, we can use trigonometry to find the change in the town's coordinates.
Let's assume the traveler starts at coordinates (0, 0). Since moving on a bearing of 055 degrees means moving clockwise from the positive x-axis, we can calculate the change in x and y coordinates using trigonometric functions.
The change in x coordinates:
Δx = distance * sin(bearing)
Δx = 200 km * sin(55°)
Δx ≈ 200 km * 0.8192
Δx ≈ 163.84 km
The change in y coordinates:
Δy = distance * cos(bearing)
Δy = 200 km * cos(55°)
Δy ≈ 200 km * 0.5736
Δy ≈ 114.72 km
Therefore, the coordinates of town P are approximately (163.84 km, 114.72 km).
Step 2: Find the coordinates of town R.
Since the traveler moves from town Q on a bearing of 155 degrees, we can again use trigonometry to calculate the change in coordinates.
Let's assume the coordinates of town Q are (0, 0). Moving on a bearing of 155 degrees means moving clockwise from the positive x-axis.
The change in x coordinates:
Δx = distance * sin(bearing)
Δx = 400 km * sin(155°)
Δx ≈ 400 km * (-0.5736)
Δx ≈ -229.44 km
The change in y coordinates:
Δy = distance * cos(bearing)
Δy = 400 km * cos(155°)
Δy ≈ 400 km * 0.8192
Δy ≈ 327.68 km
Therefore, the coordinates of town R are approximately (-229.44 km, 327.68 km).
Step 3: Calculate the distance between town P and town R.
Now that we have the coordinates of both towns, we can use the distance formula to find the distance between them.
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
Distance = √((-229.44 km - 163.84 km)^2 + (327.68 km - 114.72 km)^2)
Distance = √((-393.28 km)^2 + (212.96 km)^2)
Distance = √(154,758.61 km^2 + 45,312.16 km^2)
Distance ≈ √200,070.77 km^2
Distance ≈ 447.17 km
Therefore, the distance between town P and town R is approximately 447.17 km.
use the law of cosines to find PR
PR^2 = 200^2 + 400^2 - 2*200*400 cos80°
PR = 415 km
bearing = 330.17°