9514 1404 393
Answer:
bus: 324 ft long
P-H: 1154 miles
Step-by-step explanation:
In each case, we can use the relation that the length of an arc (s) is found by ...
s = rθ
where r is the radius and θ is the angle in radians.
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1. 2°20'50" = (2 + 20/60 + 50/3600)(π/180) radians ≈ 0.0409668 radians
Then the length of the bus is ...
(0.0409668)(1.5 mi)(5280 ft/mi) = 324 ft
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2. The difference in latitude is ...
41°17'5" -24°45'30" = 16°31'35" ≈ 0.288440 radians
Then the mileage between latitude lines is ...
s = (4000 mi)(0.288440 radians) ≈ 1154 miles
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Additional comment
Neither of these problems should be considered to be realistic. An actual bus will subtend a far smaller angle at the given distance. The distance between cities must take into account longitude as well as latitude (and the latitudes must be properly associated with the cities).
