Question

A toy car races along a circular track and is constantly 4 feet from the center of the race track. Imagine an angle with a vertex at the center of the race track that subtends the car's path. (Draw a diagram of this!)

If the racecar travels 3.6 feet in the CCW direction along the track, what is the angle's measure in radians?

___ radians

Answer 1

The angle in radians subtended by a path of a toy car on a circular track, when it travels 3.6 feet and is 4 feet from the center, is 0.9 radians.

Step-by-step explanation:

The student is asking how to determine the angle in radians when a toy car travels along a circular track. The car's path subends an angle with the center of the track at the origin, and the length of the arc travelled is given as 3.6 feet, with the radius being 4 feet. The angle in radians can be found using the formula θ = s/r, where s is the arc length and r is the radius of the circle.

Using the formula, the calculation becomes θ = 3.6 feet / 4 feet, which simplifies to θ = 0.9 radians. Therefore, the angle's measure in radians that the racecar subtends as it travels 3.6 feet in the counterclockwise direction along the track is 0.9 radians.