a high way curve is to be laid out on a circle. what radius should be used if a trailer truck is to change direction by 28 degrees in a distance of 112 meters?
arc = rØ , where Ø is in radians
28° = 28(π/180) radians = appr
112 = r (28(π/180))
r = 112(180)/(28π) = appr 229.2 m
or
112 must be 28/360 of the circumference of the circle
(28/360)(2πr) = 112
56πr = 112(360)
r = 112(360)/(56π) = appr 229.2
To determine the radius of the curve, we can use the concept of arc length and the formula for the circumference of a circle.
The arc length formula is given by:
s = rθ
where s is the length of the arc, r is the radius of the circle, and θ is the central angle in radians.
In this case, we are given that the trailer truck changes direction by 28 degrees in a distance of 112 meters. We need to convert this angle to radians, as the formula requires radians.
To convert degrees to radians, we use the formula:
radians = (π/180) * degrees
Let's calculate the angle in radians:
θ = (π/180) * 28 = 0.4887 radians (approximately)
Now we can rearrange the arc length formula to solve for the radius:
r = s / θ
Substituting the given values:
r = 112 / 0.4887
Calculating this expression, we find:
r ≈ 229.1 meters (rounded to the nearest tenth)
Therefore, the radius of the curve should be approximately 229.1 meters.