Question

An indoor staircase has a 6 inch vertical rise per step to get to the second floor of the house.  If the angle of elevation is 44 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 tenth of an inch)?

Answer 1

The staircase has a right triangle shape ABC, as shown in the picture,

with m(A)=44°, and |AB|=15 ft.

using a scientific calculator we can find that tan 44°=0.97.

Tan(A)= (opposite side)/(adjacent side)

0.97=|CB|/15

|CB|=0.97*15=14.55 (ft) = 174.6 (in)

This means that there are 176.6/6 = 29 steps, since the height of each step is 6 in.

The total horizontal space is 15 ft = 180 in,

180/29=6.2 (in)


Answer: 6.2 in