Question

​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.

Answer 1

Answer:

Distance from the base of the escalator to the point on the first floor directly below the top of the escalator = 27.5 feet

Step-by-step explanation:

Given:

Length of escalator = 30 feet

Distance between the floors = 12 feet

To find the distance from base of escalator to the point on the first floor directly below the top of the escalator  we will create the figure for the situation.

From the figure we see that a triangle ABC is formed.

We see that the Δ ABC is a right triangle.

Applying Pythagorean theorem for right triangle ABC to find the missing side.

$AB^2=BC^2+AC^2$

AB = 30 feet

BC = 12 feet

Plugging in values in the theorem.

$30^2=12^2+AC^2$

Solving for AC.

$900=144+AC^2$

Subtracting both sides by 144.

$900-144=144+AC^2-144$

$756=AC^2$

Taking square root both sides.

$\sqrt{756}=\sqrt{AC^2}$

$27.5=AC$

∴ $AC=27.5$ feet.

∴ Distance from the base of the escalator to the point on the first floor directly below the top of the escalator = 27.5 feet