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A state trooper is hidden 30 feet from a highway. One second after a truck passes, the angle between the highway and the line of observation from the patrol car to the truck is measured. See the illustration.
1 sec |30 ft
(a) If the angle measures 15°, how fast is the truck traveling? Express the answer in feet per second and in miles per hour.
(b) If the angle measures 20°, how fast is the truck traveling? Express the answer in feet per second and in miles per hour.
(c) If the speed limit is 55 miles per hour and a speeding ticket is issued for speeds of 5 miles per hour or more over the limit, for what angles should the trooper issue a ticket?
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