Question

An escalator lifts people to the second floor of a building, 26 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? A person travels __ ft. (Type an integer or a decimal.)and I only need the answer

Answer 1

The distance traveled to the top of the escalator to the bottom is 52 ft

Here, we want to calculate the distance a person on the escalator travel from the bottom to the top of the escalator

Firstly, we need a diagrammatic representation to understand this

We can form a right-angled triangle with the information given in the question.

The diagram is shown as below;

From the question, by simply calculating the hypotenuse of the right-angled triangle, we can get the distance traveled from the bottom of the escalator to the top

Let us call this distance d

We can now use the appropriate trigonometric ratio

The trigonometric ratio to use here is the sine since we have the opposite and we want to calculate the hypotenuse

Mathematically;

$\begin{gathered} \sin \text{ 30 = }\frac{26}{d} \\ \\ d\text{ = }\frac{26}{\sin \text{ 30}} \\ \\ d\text{ = }\frac{26}{0.5} \\ \\ d\text{ = 52 ft} \end{gathered}$