city A is 300km due east of city B , city C is 200km on a bearing 123 degree from city B. how far is it from C to H?

171km

To find the distance from city C to city H, we need more information. Please provide additional details such as the distance or bearing between city C and city H, or any other relevant information.

To find the distance from city C to H, we need more information about the location of city H. Can you provide any additional details?

Assuming you meant "A" instead of "H", note that if A is at (0,0), then

A to B = (300,0)
B to C = (167,-109)
So, adding them up, C is at (467,-109) and is 480 km from A