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 Z to X, we first need to find the distance from Z to Y using trigonometry.

Using the sine rule, we can find the distance from Z to Y:

sin(143°) = distance from Z to Y / 100km

distance from Z to Y = sin(143°) * 100km
distance from Z to Y = 0.7314 * 100km
distance from Z to Y = 73.14km

Now, we can find the distance from X to Y using the Pythagorean theorem:

distance from X to Y = sqrt(200km^2 - 73.14km^2)
distance from X to Y = sqrt(40000km^2 - 5345.7796km^2)
distance from X to Y = sqrt(34654.2204)
distance from X to Y = 186.29km

Now, we can find the distance from Z to X using the cosine rule:

cos(143°) = distance from Z to X / distance from Z to Y
distance from Z to X = cos(143°) * 186.29km
distance from Z to X = -0.7314 * 186.29km
distance from Z to X = -136.23km

The distance from Z to X is 136.23km.