# Math

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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1. I need an answer to the question

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2. 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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4. 315

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5. 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

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6. The bearing of q from p is 180°+70°=250°

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