Question

43 an escalator runs from the first floor of a shopping mall to the second floor. the length of the escalator is 30 feet and the distance between the floors is 12 feet. find the distance from the base of the escalator to the point on the first floor directly below the top of the escalator. round your answer to the nearest tenth if necessary. image of a right triangle representing the escalator, height 12 ft, hypotenuse 30 ft a 27 feet b 18 feet c 32.3 feet d 27.5 feet

Explanation:

Step1: Identify the right triangle

The escalator, the vertical distance between floors, and the horizontal distance form a right triangle. Let the horizontal distance be \( x \), the escalator length (hypotenuse) be \( c = 30 \) feet, and the vertical distance be \( a = 12 \) feet.

Step2: Apply the Pythagorean theorem

The Pythagorean theorem is \( a^2 + x^2 = c^2 \). Substitute \( a = 12 \) and \( c = 30 \):

$$ 12^2 + x^2 = 30^2 $$

$$ 144 + x^2 = 900 $$

Step3: Solve for \( x^2 \)

Subtract 144 from both sides:

$$ x^2 = 900 - 144 $$

$$ x^2 = 756 $$

Step4: Solve for \( x \)

Take the square root of 756:

$$ x = \sqrt{756} \approx 27.5 $$

Answer:

D. 27.5 feet