Town X is 200km due east of town Y. Town Z is 100km on a bearing of 143° from town Y. How far is it from Z to X

Answer 1

To find the distance from town Z to town X, we can break it down into two components: the north-south component and the east-west component.

First, we need to find the north-south component. We know that town Z is 100km away from town Y at a bearing of 143°. This means that the north-south component is 100km * cos(143°) = -47.74 km. The negative sign indicates that the north-south component is to the south.

Next, we need to find the east-west component. We know that town X is due east of town Y, which means there is no east-west displacement from Y to X.

To find the total distance from Z to X, we can use the Pythagorean theorem: distance = sqrt((east-west component)^2 + (north-south component)^2)

distance = sqrt(0^2 + (-47.74)^2) = sqrt(2279.44) ≈ 47.74 km

Therefore, the distance from town Z to town X is approximately 47.74 km.