Find the area of the triangle created by three posts X, Y and Z, where X bears 072o from Y and Z bears 157o from Y and the distance from Y to X and Z is 520m and 965m respectively (1ha = 10 000m2)

Question

Find the area of the triangle (in hectares) created by three posts X, Y and Z, where X bears 072o from Y and Z bears  157o from Y, and the dist ance from Y to X and Z is 520m and 965m respectively. (1ha = 10 000m2)

Answer 1

In the triangle XYZ, ∠XYZ=157-72=85°, XY=520m and YZ=965m.

We have 2 sides and the included angle so the area=½(520)(965)sin85=249945.25m² approx. This is 24.9945 hectares approx. That's 25ha to the nearest hectare.