A village y is 15km from a point x on a bearing of 025 decree another village z is 20km from x on a bearing of 115 decree calculate the point yz

Answer 1

To calculate the distance between village y and village z (yz), we can use the Law of Cosines.

First, we need to find the interior angle at point x formed by the lines xy and xz.

Angle yxz = 180 - (25 + 115) = 40 degrees

Now, we can use the Law of Cosines:

yz^2 = xy^2 + xz^2 - 2(xy)(xz)cos(angle yxz)
yz^2 = 15^2 + 20^2 - 2(15)(20)cos(40)
yz^2 = 225 + 400 - 600cos(40)
yz^2 = 625 - 600(0.7660)
yz^2 = 151.40
yz ≈ √151.40
yz ≈ 12.31 km

Therefore, the distance between village y and village z is approximately 12.31 km.