Final answer:
The radius of a turn cannot be determined from the angle alone without additional information such as speed or force. However, the ideal banking angle for a turn on a highway can be found using the formula θ = tan-1(v2/rg).
Step-by-step explanation:
To determine the radius r of the turn given the angle θ, we must know additional parameters such as the speed of the vehicle or force involved in the turn. However, based on the information provided in your question, we can discuss the relationship between the banking angle and the radius of a turn for an ideally banked roadway. The formula to calculate the ideal banking angle θ for a turn is derived from equating the centripetal force required for a turn and the component of gravitational force acting down the slope of the banking angle. The formula is θ = tan-1(v2/rg) where v is the velocity, r is the radius, and g is the acceleration due to gravity.
For instance, to calculate the banking angle for a gentle turn with a radius of 1.20 km at a speed limit of 105 km/h, you'll use the formula provided.