y is 60km away from x on a bearing of 135 degree.Z is 80km away from x on a bearing of 225 degree find (a)distance of z from y (b) bearing of z from y
angle YXZ is 90° so YZ = 100 (3-4-5 triangle)
relative to X,
Y = (60/√2 , -60/√2)
Z = (-80/√2 , -80/√2)
so, relative to Y, Z is at (-140/√2, -20/√2) for a bearing of
270° - arctan(1/7) = 261.86°
I did not know it,pls explain it to me and give me the solution
Pls explain to me
To find the distance between points, we can use the Pythagorean theorem. The bearing angle can be used to find the relative x and y components of the distances.
(a) Distance from Z to Y:
To find the distance between Z and Y, we need to break down the distance into x and y components.
From point X, the bearing of 135 degrees means we are moving 135 degrees counterclockwise from the positive x-axis.
To find the x-component of the distance between X and Y, we can use the formula: x = distance * cos(angle).
x = 60 km * cos(135 degrees) = -42.43 km (rounded to two decimal places)
The negative sign indicates that the x-component is in the negative direction.
To find the y-component of the distance between X and Y, we can use the formula: y = distance * sin(angle).
y = 60 km * sin(135 degrees) = 42.43 km (rounded to two decimal places)
Therefore, the distance from Z to Y can be found using the Pythagorean theorem:
Distance(ZY) = sqrt((y2 - y1)^2 + (x2 - x1)^2)
= sqrt((42.43 km)^2 + (-42.43 km)^2)
= sqrt(1800 km^2)
≈ 42.43 km (rounded to two decimal places)
So, the distance from Z to Y is approximately 42.43 km.
(b) Bearing of Z from Y:
To find the bearing of Z from Y, we can use the inverse tangent (arctan) function to find the angle between the positive x-axis and the line connecting Y and Z.
Bearing(ZY) = atan((y2 - y1) / (x2 - x1))
Since we are finding the bearing of Z from Y, the X-coordinate of Y becomes X-coordinate(Z), and the Y-coordinate(Y) becomes Y-coordinate(Z).
Bearing(ZY) = atan((-42.43 km) / (42.43 km))
≈ atan(-1)
≈ -45 degrees (rounded to nearest whole number)
However, the bearing is typically measured clockwise from the positive x-axis. So we need to convert the bearing to a clockwise bearing by subtracting it from 360 degrees:
Bearing(ZY) = 360 degrees - 45 degrees
= 315 degrees
Therefore, the bearing of Z from Y is approximately 315 degrees.
a. d = 80km[225] - 60km[135o].
X = 80*sin225 - 60*sin135 = -99 km.
Y = 80*Cos225 - 60*Cos135 = -14 km.
d = sqrt(X^2 + Y^2) = 100 km.
b. Tan A = X/Y.
A = 82o W of S. = 262o CW from +y-axis(bearing).