The bearing of x from y is 045°and the bearing of z from y is 145°,where x,y and z are three points in the plane.lf y is equidistant from x and z,find the bearing of z from x.
what are the given answers?
From North
x is 45 deg clockwise from north
z is 145 clockwise from north so 100 clockwise from YX
so angle xyz =100
the two lengths are equal so yz=yx and
2(angles) + 100 = 180
so the other two angles are 40
z to y = 145 + 180 = 325
add 40 for z to x
365, which is 5 degrees on your compass
The triangle internal angle at y is 145-45=100 since the triangle is isosceles, the internal angles at x and z are both (180-100)/2=40:then the bearing of z from x is the bearing of y From x less the internal angle at x(45+180)-40=180 . therefore z from x is 185
Well, well, well. It seems we have a little geometry puzzle, don't we? Let's put on our thinking caps and solve this riddle.
Since point y is equidistant from points x and z, we can conclude that triangle xyz is an isosceles triangle.
Now, let's focus on finding the bearing of z from x. Remember the good old saying "opposites attract"? Well, it applies here too!
Since x and z are equidistant from y, we can conclude that the bearing of z from x is just the opposite of the bearing of x from z. In other words, it's like flipping those numbers upside down.
So, if the bearing of x from z is 045°, the bearing of z from x will be 180° - 045° = 135°.
Voila! The bearing of z from x is 135°. Now that's what I call a triangle-tastic solution!
To find the bearing of point z from point x, we need to determine the angle formed by the line connecting x and z with respect to the north.
Given:
1. The bearing of x from y is 045°.
2. The bearing of z from y is 145°.
3. Point y is equidistant from x and z.
Let's break down the problem step by step:
Step 1: Determine the direction from x to y.
The bearing of x from y is 045°. This means that if you face directly from y towards x, you are facing at a 45° angle clockwise from the north direction.
Step 2: Determine the direction from y to z.
The bearing of z from y is 145°. This means that if you face directly from y towards z, you are facing at a 145° angle clockwise from the north direction.
Step 3: Determine the angle from x to z.
Since point y is equidistant from x and z, we can conclude that the angle formed by the line connecting x and z is the same as the difference between the bearings of x from y and z from y.
So, to find the bearing of z from x, subtract the bearing of x from y (045°) from the bearing of z from y (145°):
145° - 045° = 100°
Therefore, the bearing of z from x is 100°.