Question

1) An i staircase has a 10 inch vertical rise per step to get to the second floor of the house. If the angle of elevation is 30.20 degrees and there are 12 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).

A and b are both questions regaurding the stairs. Answer both, and show your work to recieve brainliest.

Answer 1

Answer:

A)

Each landing is about 17 inches.

B)

The vertical rise from Floor 1 to Floor 2 is about 7 feet.

Step-by-step explanation:

Please refer to the attachment below. (I accidentally wrote 30.30 instead of 30.20. Please ignore that and sorry for any confusion.)

Part A)

So, we want to find the length of $\ell$.

Note that the angle of elevation, the vertical height, and $\ell$ form a right triangle.

Since the vertical height opposite to our angle is 10, and we want to find the adjacent height, we can use the tangent ratio:

$\displaystyle \tan(x^\circ)=\frac{\text{Opposite}}{\text{Adjacent}}$

Therefore:

$\displaystyle \tan(30.20)=\frac{10}{\ell}$

Solve for $\ell$. Cross-multiply:

$\displaystyle \ell\tan(30.20)=10$

So:

$\displaystyle \ell=\frac{10}{\tan(30.20)}=17.1817...\approx17\text{ inches}$

The landing space per step is about 17 inches.

Part B)

We know that there are a total of 12 feet of horizontal space total for each landing.

12 feet is equivalent to (12)(12) = 144 inches.

Since each landing is 17.1817... inches, this means that we have 144/(17.1817...) = 8.38... or about 8 steps.

Since the vertical rise of each step is 10 inches, the vertical rise from the 1st Floor to the second will be 8(10) or 80 inches or 80/12 = 6.666... or about 7 feet.