Answer:
10 5/8 km
Step-by-step explanation:
Name the point 8 km north of the hospital point N. Then triangle NHC is similar to triangle AHX, where A is the point 5 km north of the hospital.
This means that ...
HX/HC = HA/HN = 5/8
HX = (5/8)HC
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The distance HC can be found using the Pythagorean theorem. It tells you ...
HC^2 = HN^2 +NC^2 = 8^2 +15^2 = 289
HC = √289 = 17
so ...
HX = (5/8)(17) = 10 5/8
The distance from the hospital to X is 10 5/8 km.
