Presume that a ladder is put upright against a wall. Let variables length and angle store the length of the ladder and the angle that it forms with the ground as it leans against the wall. Write a Python program to compute the height reached by the ladder on the wall for the following values of length and angle: a) 16 feet and 75 degrees b) 20 feet and 0 degrees c) 24 feet and 45 degrees d) 24 feet and 80 degrees

Presume that a ladder is put upright against a wall. Let variables length and angle store the length of the ladder and the angle that it forms with the ground as it leans against the wall. Write a Python program to compute the height reached by the ladder on the wall for the following values of length and angle:

a) 16 feet and 75 degrees

b) 20 feet and 0 degrees

c) 24 feet and 45 degrees

d) 24 feet and 80 degrees

Here is a Python program to compute the height reached by a ladder on the wall for given lengths and angles:

import math

# Function to calculate the height reached by the ladder
def height_reached(length, angle_degrees):
    angle_radians = math.radians(angle_degrees)  # Convert angle to radians
    height = length * math.sin(angle_radians)   # Calculate height using sine
    return height

# Test cases
ladder_cases = [
    (16, 75),
    (20, 0),
    (24, 45),
    (24, 80)
]

for length, angle in ladder_cases:
    height = height_reached(length, angle)
    print(f"Length: {length} feet, Angle: {angle} degrees, Height reached: {height:.2f} feet")

Explanation of the Code:

1. Import the math module: This module provides access to mathematical functions like sin which calculates the sine of an angle.

2. Define a function height_reached:

   • Convert the angle from degrees to radians using math.radians.

   • Calculate the height using the formula $ \text{height} = \text{length} \times \sin(\text{angle in radians}) $. The sine function is used to find the vertical component of the ladder length.

3. Iterate through the test cases:

   • Compute and print the height reached by the ladder for each (length, angle) pair.

Output:

Length: 16 feet, Angle: 75 degrees, Height reached: 15.45 feet
Length: 20 feet, Angle: 0 degrees, Height reached: 0.00 feet
Length: 24 feet, Angle: 45 degrees, Height reached: 16.97 feet
Length: 24 feet, Angle: 80 degrees, Height reached: 23.64 feet

This will show the height on the wall reached by the ladder for the specified lengths and angles.