Astate trooper is hidden 30 feet from a highway. one second after a truck passes; the angle θ between the highway and the line of observation from the patrol car to the truck is measured.

a. if the angle measures 15˚, how fast is the truck traveling?

b. if the angle measures 20˚, how fast is the truck traveling?

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 angle should the trooper issue a ticket?

Givens

This problem models a right triangle, which is attached.

So, if , we apply trigonometric reasons to find the speed of the truck

Where is the horizontal distance of the truck

So, if time of the truck is one second, assuming that is a constant movement, the speed would be

If , doing the same process, we have

So, the speed would be

First, we need to tranform the speed into feet per second. We know that 1 mile equals 5280 feet, and 1 hour equals 3600 seconds,

So, the horizontal distance of the truck in this case is 80.67 feet, because, the trooper saw it after 1 second.

Now, we use the trigonometric relation to find the angle

Therefore, the angle limit is 20.4° approximately, that means all angles more than this issue a ticket for excess of speed.

4

step-by-step explanation: