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Asked by Sarah

X, Y and Z are three points on a map. Y is 75 km and on a bearing of 190 from x. Z is on a bearing of 140 from Y. Z is due south of x Calculate the distance between x and Z rounded to 1 dp?

First draw a diagram. You will see that XYZ form a scalene triangle. Now to work out the distance from X, you will want to find out the internal angles of the triangle. You know that Z is on a bearing due 140 from Y, since Z is due south of X, You can continue to draw the line from YZ and you will see that the angles on the line add up to 180 degrees. Therefore YZX is 40 deg. Since Y is bearing 190 deg from X, we can just do 190-180=10 to find out the internal angle YXZ. Then we can calculate the final angle 180-40-10=130. You can then use A/sina=B/sinb to find the distance ZX. 75/sin40 x sin130=89.38km

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Adam Maniar
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