Question

A 90-foot escalator rises a vertical distance of 45 feet, as shown in the diagram below.

What is the measure of the angle identified with a question mark in the diagram?

30°
45°
60°
90°

Answer 1

Answer: 30

Explanation:

The correct answer is 30

Answer 2

You haven't provided a diagram, so I will calculate both acute angles and add an image to show where they are.

Angle the escalator makes with the floor

`\implies sin(\theta)=(45)/(90)=\frac12`

`\implies \theta=30 \textdegree`

Angle the escalator makes with the wall (vertical)

`\implies cos(\theta)=(45)/(90)=\frac12`

`\implies \theta=60 \textdegree`