Hot girl with cool car

Question

Problem Description
Huahua is a beautiful girl. Since she is still single, you can imagine how many boys want to dating with her on Saint Valentine's Day! Huahua is a clever girl, she do know well how to pick a boy by the way she like.

Unlike other girls, Huahua have a special hobby, that she is a professional fan of automobile race game. Her interest ranging widely from real car racing such as Formula 1, Dakar Rally, Le Mans World Endurance Championship, even to virtual games ,for instance, Need for Speed. Just because of this, Huahua is extremely popular in boys' eyes. It is a universally truth that hot girl with powerful cool car, everybody becomes blood surge!

Now Huahua got an idea. You know in professional racing game, choose a most suitable path when steer is very important. It can even decide the result. Driver must know very well about the road condition, control car speed at the braking point before entering curve, and turn wheel immediately at the beginning of the curve. But when is the right time to turn? Which is the best path? Huahua rise this technical problem to you.

Suppose there is a racing track shown in Graph 1, and we are facing a regular curve. Huahua will tell you the road condition: w (Unit: Meter) stands for the track wide, r (Unit: Meter) for the turning radius (inside the track), and θ ( 0°< θ <=180°) for the the angle of the curve we discussing. Since larger turning radius can provide driver better control experience and gain more time, your task is to tell Huahua the largest turning radius driver can pick. The one who first slove this problem will become the lucky dog and able to dating with Huahua on Saint Valentine's Day!

Graph 1: Racing Track

Input
There are multiple cases, please process to End of File.
For each case:
Three postive real number: r, w, θ, as described above.

Output
For each case, you are required to calculate R ( Unit: Meter ), which is the largest turning radius driver can pick. Round to 3 after point.

Sample Input
30 70 90

Sample Output
268.995

Answer 1

以下回答参考 皆我百晓生、券券喵儿 等免费微信小程序相关内容作答，并由本人整理回复。

# read data
data <- read.table(header = TRUE, text = "30 70 90\n")

# function to find the largest turning radius
largest_turning_radius <- function(r, w, theta){
  # convert degrees to radians
  theta_rad <- theta * pi / 180
  
  # calculate the maximum possible radius
  max_radius <- sqrt(w^2 + r^2 - 2*w*r*cos(theta_rad))
  
  return(max_radius)
}

# loop through each case
for(i in 1:nrow(data)){
  r <- data[i, 1]
  w <- data[i, 2]
  theta <- data[i, 3]
  output <- largest_turning_radius(r, w, theta)
  print(paste("The largest turning radius for a curve with width ", r, " meters, radius of curvature ", w, " meters, and angle of the curve ", theta, " degrees is ", format(output, digits = 3)))
}

This code reads the input data from a table, converts the angles from degrees to radians, calculates the maximum possible radius using the formula derived from the geometry of a circle, and outputs the result rounded to three decimal places.