Animated prop with ultrasonic sensor and servo motor

Hello! I am making a prop that raises his arm the closer you get to it using a ultrasonic sensor and servor motor. I already have it set when you go in front of the sensor, it goes all the way 180* (or whatever * i figured out how to set it to) but i want it to gradually raise up the closer you get to it.

The code im using:

#include <Servo.h>

// constants won't change
const int TRIG_PIN  = 6;  // Arduino pin connected to Ultrasonic Sensor's TRIG pin
const int ECHO_PIN  = 7;  // Arduino pin connected to Ultrasonic Sensor's ECHO pin
const int SERVO_PIN = 9; // Arduino pin connected to Servo Motor's pin
const int DISTANCE_THRESHOLD = 100; // centimeters

Servo servo; // create servo object to control a servo

// variables will change:
float duration_us, distance_cm;

void setup() {
  Serial.begin (9600);       // initialize serial port
  pinMode(TRIG_PIN, OUTPUT); // set arduino pin to output mode
  pinMode(ECHO_PIN, INPUT);  // set arduino pin to input mode
  servo.attach(SERVO_PIN);   // attaches the servo on pin 9 to the servo object
  servo.write(0);
}

void loop() {
  // generate 10-microsecond pulse to TRIG pin
  digitalWrite(TRIG_PIN, HIGH);
  delayMicroseconds(10);
  digitalWrite(TRIG_PIN, LOW);

  // measure duration of pulse from ECHO pin
  duration_us = pulseIn(ECHO_PIN, HIGH);
  // calculate the distance
  distance_cm = 0.017 * duration_us;

  if (distance_cm < DISTANCE_THRESHOLD)
    servo.write(180); // rotate servo motor to 90 degree
  else
    servo.write(0);  // rotate servo motor to 0 degree

  // print the value to Serial Monitor
  Serial.print("distance: ");
  Serial.print(distance_cm);
  Serial.println(" cm");

  delay(100);
}

I saw another post say that you need to change the distance to an angle? I am new here and any help would be great. Thank you!

Try the map() function. You can translate the distance value directly to a servo value.