Question

2) An outdoor staircase has a total vertical elevation of 11 feet from the road level to the front entrance of a building. If the angle of elevation is 37 degrees and the landing of each step is 8 inches, answer the following questions showing each step of your work:
a) What is the vertical rise per step (in inches, rounded to the nearest whole inch)?


b) Find the number of steps needed to climb from road level to the front entrance.



3) A staircase of steps in a swimming pool has a vertical rise of 14 inches per step and a landing of 20 inches. Answer the following questions showing each step of your work:
a) What is the angle of elevation (rounded to the nearest whole degree)?


b) If the landing of each step is changed to 17 inches and the elevation of each step to 21 inches, what is the new angle of elevation for the staircase (rounded to the nearest whole degree)?


Please help me with these im confused.

Answer 1

2a

tan37=r/8

r=8tan37

r≈6 in rise per step (to nearest whole inch)

2b

11*12/6=22 steps needed to climb the 11 ft to the entrance

...

3a

tanα=14/20

α=arctan(7/10)

α≈35° (to nearest whole degree)

..

3b

tanα=21/17

α=arctan(21/17)

α≈51° (to nearest degree)