Question

1) An indoor staircase has a 12 inch vertical rise per step to get to the second floor of the house. If the angle of elevation is 41 degrees and there are 15 feet of horizontal space total for each of the landings combined, answer the following questions showing each step of your work:
a) What is the landing space per step (in inches, rounded to the nearest inch)?


b) Find the vertical rise from the 1st floor to the 2nd floor (in feet, rounded to the nearest foot).

Answer 1

The landing space per step is 14 inches while the vertical rise is 13 feet.

Trigonometric ratio

Trigonometric ratio is used to show the relationship between the sides and the angles of a right angled triangle.

From the question:

Angle of elevation = 41°

Let d represent the landing space per step, hence using trigonometric ratio:

tan(41) = 12 inches / d

d = 14 inches

Also, let h represent the vertical rise, hence:

tan(41) = h / 15 feet

h = 13 feet

The landing space per step is 14 inches while the vertical rise is 13 feet.

Find out more on Trigonometric ratio at: brainly.com/question/4326804