Math CentralQuandaries & Queries


Rita, a student:

A state trooper is hidden 30 feet from a highway. One second after a truck passes, the angle theta between the highway and the line of observation from the patrol car to the truck is measured.

(a) If the angle measures 15 degrees, how fast is the truck traveling? Express the answer in feet per second and miles per hour.

Hi Rita,

I am going to assume that the state trooper is 30 feet from the speeding truck:

The position when the speeding truck is 30 ft away and the position 1 second later form a right triangle. Now you can use trigonometry to solve for the distance the truck travels in 1 second to find the speed.

Hope this helps,


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