The bearing of x from y is 070 and the bearing of z from y is 160, where x, y, and z are three points in the plane .if y is equidistant from x and z, find the bearing of z from x
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315
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180 less 90 is 90 therefore the triangle is issoscless hence 90 divided by 2 gives 45 also 360 less 45 is 315 final answer
The bearing of q from p is 180°+70°=250°
180+70 =250
180 less 90 is 90 therefore the triangle is issoscless hence 90 divided by 2 gives 45 also 360 less 45 is 315 final answer
To find the bearing of point z from point x, we need to determine the angle formed between the line connecting x and z and the north direction.
Given:
- The bearing of x from y is 070. This means that the angle formed between the line connecting y and x and the north direction is 70 degrees clockwise.
- The bearing of z from y is 160. This means that the angle formed between the line connecting y and z and the north direction is 160 degrees clockwise.
Since y is equidistant from x and z, we can conclude that the angle formed between the line connecting x and y and the line connecting y and z is 180 degrees (a straight line).
To find the bearing of z from x, we need to determine the angle formed between the line connecting x and z and the north direction. We can use the angle between y and z (160 degrees) and subtract it from the angle between y and x (70 degrees).
The calculation would be as follows:
Angle of z from x = Angle of z from y - Angle of x from y
Angle of z from x = 160 - 70 = 90 degrees.
Therefore, the bearing of z from x is 090.
I assume that those are compass bearings, clockwise from North.
In that case x is one unit away from y at the origin, 20 degrees above the x axis (East)
z is 160 - 90 = 70 degrees below the x (East axis), again one unit of distance.
Lo and behold, the angle xyz is 20 + 70 = 90 degrees
That means the triangle angles at x and z are each 45 degrees, which might be useful.
call the intersection of xz with the x axis w
then y w x = 180 - 45 - 20 = 115
that is 115 - 90 = 25 deg clockwise from north
so zw direction is 25
so xz direction = 180 + 25 = 205
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