Question

An escalator lifts people to the second floor of a building, 25 ft above the first floor. The escalator rises at a 30° angle. To the nearest foot, how far does a person travel from the bottom to the top of the escalator?

Answer 1

Answer:

50 feet

Step-by-step explanation:

Given:

Vertical height of lift by escalator (h) = 25 ft

Angle of inclination of escalator (x) = 30°

Now, the person traveling along the escalator is equal to the length of the escalator from bottom to top.

Now, a triangle can be constructed using the above scenario.

Consider a right angled triangle ABC with:

AB → Vertical height of escalator = 25 ft

AC → Length of escalator = ?

Now, using trigonometric ratio for sine, we can find the length AC.

This gives,

$\sin (x)=\frac{AB}{AC}\\\\\sin(30)=\frac{25}{AC}\\\\AC=\frac{25}{\sin(30)}\\\\AC=\frac{25}{0.5}=50\ ft$

Therefore, the distance of travel of a person from bottom to top of the escalator is 50 feet.