Question

Michelle's hamster has gotten too heavy to climb through its tube if it is sloped at more than a 24 ° angle. If the tube is 32 inches long, how high could Michelle raise the tube at one end so that her hamster can still climb through it? Estimate your answer to two decimal places.

Answer 1

Michelle can raise the end of the tube to a height of approximately 13.01 inches to maintain a slope of 24 degrees, using the sine function to calculate the height based on the tube's length.

Step-by-step explanation:

Michelle's hamster can climb through a tube sloped at an angle of 24 degrees. To find the maximum height Michelle can raise the tube while maintaining this angle, we can use the sine function, which relates the angle of a right triangle to the ratio of the length of the opposite side (the height in this case) to the hypotenuse (the length of the tube).

The formula we will use is:

Height = Hypotenuse × sin(Angle)

Let's plug in the values:

Height = 32 inches × sin(24 degrees)

Using a calculator, we find:

Height ≈ 32 inches × 0.4067

Height ≈ 13.01 inches

Therefore, Michelle can raise the end of the tube to a height of approximately 13.01 inches to maintain the maximum angle of 24 degrees for her hamster to be able to climb through.