Question

For driving safety, it is important for each driver to think about how far their car will travel by the time they finish a maneuver. Suppose a car is moving forward in a straight path. To change lanes, the driver must turn the steering wheel slightly. This causes the car to travel in a direction that points 2.1° away from the forward direction. Once the lane change is complete, the driver turns the steering wheel so the car moves forward again. If a lane on the highway is 12 feet wide, how far forward in feet will a car travel to change lanes? Enter your answer to the nearest tenth (one decimal place). horizontal distance 2.1 vertical 87.9 12 ft distance 121 vertical distance horizontal distance

Answer 1

We have to calculate the side "horizontal distance" of the triangle.

By definition,

tan(angle) = opposite/adjacent

Replacing with data from the picture,

tan(2.1°) = 12/x

x = 12/tan(2.1°)

x = 327.3 ft