Y is 60km away from x on a bearing of 135 degrees. Z is 80km away from x on a bearing of 225 degrees. Find
a. The distance of z from y
b. The bearing of z from y
note that angle ZXY is a right angle.
(a) |YZ| = 100
(b) from Y, ∆y/∆x = (-20/√2)/(-140/√2) = 1/7
the reference angle is 8.13°
So, referring to your diagram, the bearing of Z from Y is 270-8.13 = 261.87°
All angles are measured CW from +Y axis
a. d = 80km[225o] - 60km[135o].
d = -56.6-56.6i - (42.4-42.4i) = -99 - 14i = 58.3 km.
b. TanA = X/Y = -99/-14.
A = 76o W. of S. = 256o CW.
Correction:
a. d = -99 - 14i = 100 km.
b. A = 82o W. of S. = 262o CW from +y-axis.
To find the distance between points Y and Z, we can use the triangle formed by points X, Y, and Z. To solve this problem, we will use the concept of vector addition.
Step 1: Draw a diagram:
- Draw point X as the origin (0,0) on a coordinate plane.
- Measure 60km on a bearing of 135 degrees from X and mark it as point Y.
- Measure 80km on a bearing of 225 degrees from X and mark it as point Z.
Step 2: Find the coordinates of points Y and Z:
- Using trigonometry, find the horizontal and vertical components of the distances for Y and Z.
For Y:
- Horizontal component: 60km * cos(135°)
- Vertical component: 60km * sin(135°)
- The coordinates of point Y will be (X + horizontal component of Y, Y + vertical component of Y).
For Z:
- Horizontal component: 80km * cos(225°)
- Vertical component: 80km * sin(225°)
- The coordinates of point Z will be (X + horizontal component of Z, Y + vertical component of Z).
Step 3: Calculate the distance between points Y and Z:
- Use the distance formula: distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
- Substitute the coordinates of points Y and Z into the formula to find the distance between them.
Step 4: Calculate the bearing of Z from Y:
- Use the formula: bearing = arctan((y2 - y1) / (x2 - x1))
- Substitute the coordinates of points Y and Z into the formula to find the bearing of Z from Y.
Following these steps, you can find:
a. The distance of Z from Y.
b. The bearing of Z from Y.