Question

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, rounded to the nearest tenth.

Answer 1

To find the distance from the base of the escalator to the point on the first floor below the top, we can use the Pythagorean theorem. The distance is approximately 27.5 feet.

Step-by-step explanation:

To find the distance from the base of the escalator to the point on the first floor directly below the top of the escalator, we can use the Pythagorean theorem.

Let's say the distance from the base of the escalator to the point on the first floor is 'x' feet.

According to the Pythagorean theorem, the sum of the squares of the lengths of the two shorter sides of a right triangle is equal to the square of the length of the hypotenuse.

In this case, the two shorter sides are the height difference between the floors (12 feet) and the distance from the base of the escalator to the point on the first floor ('x' feet).

So, the equation would be: 12^2 + x^2 = 30^2

After simplifying and solving for 'x', we get: x = √(900-144) = √756 = 27.5 feet (rounded to the nearest tenth).