The bearing of X from Y is 045 and of Z from Y is 145 ,where X,Y and Z are three points in a plane .if You is equidistant from X and Z find the bearing of Z from X
Easy to make a sketch to get the triangle.
YX and YZ must form a 100° angle, and YX = YZ , so you have an isosceles triangle.
Remember North and South are vertical lines.
Let me know what you get
Don't understand the question
To find the bearing of Z from X, we need to use the concept of bearing angles in coordinate geometry.
Given:
Bearing of X from Y = 045
Bearing of Z from Y = 145
Here are the steps to find the bearing of Z from X:
1. Draw a plane and mark the three points X, Y, and Z.
- X, Y, and Z are not collinear, as given that Y is equidistant from X and Z.
2. From the given information, we know that the bearing of X from Y is 045. This means that the angle between the line XY and the north direction is 45 degrees clockwise.
3. Similarly, the bearing of Z from Y is 145. So, the angle between the line YZ and the north direction is 145 degrees clockwise.
4. Since Y is equidistant from X and Z, we can draw a line perpendicular to XY passing through Y and label it as line m.
5. Line m will bisect the angle between XY and YZ.
6. Label the point of intersection of line m and YZ as point P.
7. Now, we have a right triangle XPY (right angle at point P), with sides XY and YP.
8. The angle YPX is obtained by subtracting the bearing of X from Y (045) from 180 degrees, as it is a straight angle.
9. Therefore, angle YPX = 180 - 45 = 135 degrees.
10. Since X is a right angle, we have a triangle XZY with sides XZ, YZ (from given information), and angle YZX (180 - 145 = 35 degrees).
11. We need to find the bearing of Z from X, which is the angle between the line XZ and the north direction. This angle can be found by subtracting angle YPX (135 degrees) from angle YZX (35 degrees).
12. Therefore, the bearing of Z from X = 35 - 135 = -100 degrees (as measured clockwise from the north direction).
So, the bearing of Z from X is -100 degrees.
To find the bearing of Z from X, we need to determine the direction or angle from X to Z.
First, let's understand what bearing means. Bearing is the direction from one point to another, typically measured in degrees clockwise from the north direction. In this case, the bearing of X from Y is 045, which means X is located 45 degrees clockwise from the north direction when looking from Y. Similarly, the bearing of Z from Y is 145, which means Z is located 145 degrees clockwise from the north direction when looking from Y.
Since You is equidistant from X and Z, it means that X, You, and Z form an isosceles triangle with You as the apex. In this triangle, the base is formed by the line segment XZ, and the apex is formed by the point You.
To find the bearing of Z from X, we can use the fact that the sum of the three interior angles in any triangle is always 180 degrees.
Let's calculate:
1. The bearing of X from Y is 045, so the angle between XY and the north direction is also 045 degrees (as both angles have the same measure).
2. The bearing of Z from Y is 145, so the angle between YZ and the north direction is 145 degrees.
3. The sum of the angles at X and Z in an isosceles triangle is 180 - the angle at You.
Since You is the apex of the isosceles triangle, the angle at You is the same as the angle between YX and YZ. Therefore, the angle at You can be calculated as:
180 - (angle between YX and the north direction) - (angle between YZ and the north direction)
Angle at You = 180 - 045 - 145 = 180 - 190 = -10 degrees
Note that in this case, the angle is negative because it is measured clockwise from the north direction.
Now we know that the angle at You is -10 degrees. Since X is on one side of You and Z is on the other side, the bearing of Z from X is equal to:
(angle between YX and the north direction) + (angle at You)
Bearing of Z from X = 045 + (-10) = 035 degrees.
Therefore, the bearing of Z from X is 035 degrees.