Final answer:
To calculate the hypotenuse given an angle and a side length in Python, use the cosine function after converting the angle from degrees to radians. If only side lengths are known, apply the Pythagorean theorem. The provided Python program demonstrates finding the hypotenuse with the trigonometric approach.
Step-by-step explanation:
To find the length of the hypotenuse given an angle and a side length in a right triangle, we can use either trigonometric functions or the Pythagorean theorem, depending on the information available. In Python, you can use the math module to perform these calculations. Here is a sample Python program that assumes you have the length of one side (adjacent to the angle) and the angle value itself, and it will calculate the hypotenuse using the cosine of the angle:
import math
def find_hypotenuse(adjacent, angle_degrees):
# Convert angle from degrees to radians
angle_radians = math.radians(angle_degrees)
# Use the cosine to find the hypotenuse
hypotenuse = adjacent / math.cos(angle_radians)
return hypotenuse
# Example usage
side_length = float(input('Enter the length of the side adjacent to the angle: '))
angle = float(input('Enter the angle in degrees: '))
hypotenuse_length = find_hypotenuse(side_length, angle)
print(f'The length of the hypotenuse is: {hypotenuse_length:.2f}')
Note that this program converts the angle from degrees to radians because the math.cos function expects the angle in radians. Additionally, the Pythagorean theorem is used to calculate the hypotenuse in some of the references. The theorem states that in a right-angled triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b): c = √(a² + b²).