some hints to get you going:
#1
tan 25° = .466
So, each step is .466 as high as it is wide.
#2
tan 36.8° = 3/4
#3
tanθ = 12/15 = 4/5
θ = 38.7°
arctan(10/7) = 55°
A carpenter is building a staircase using his knowledge of right angles. The steps have a horizontal landing and a vertical rise causing each step to be a right triangle cut out. Depending on the purpose, steps may be adjusted by the angle of elevation which determines the pitch or steepness of the climb. A carpenter must factor in an appropriate amount of room on the landing for a person to have room for their foot on the step. Using this information, calculate the following questions below. (You must show all work to receive full credit)
1) Outdoor steps generally require larger landings and lower pitches. A particular outdoor staircase climbs a total vertical elevation of 13 feet from the road level to the front entrance of a building. If the angle of elevation is to be 25 degrees and the landing of each step is to be 28 inches, calculate the following (you must show all work to receive full credit):
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.
2) Indoor steps generally are steeper and have smaller landings. A staircase has a 9 inch vertical rise per step to get to the second floor of a house. If the angle of elevation is 36.8 degrees and there are 16 feet of horizontal space total for each of the landings combined, calculate the following questions (you must show all work to receive full credit):
2) Indoor steps generally are steeper and have smaller landings. A staircase has a 9 inch vertical rise per step to get to the second floor of a house. If the angle of elevation is 36.8 degrees and there are 16 feet of horizontal space total for each of the landings combined, calculate the following questions (you must show all work to receive full credit):
a) What is the landing space per step? (In inches rounded to the nearest tenth)
b) Find the vertical rise from the 1st floor to the 2nd floor to the nearest foot.
3) A third staircase in a swimming pool has a landing of 15 inches and a vertical rise of 12 inches per step. To the nearest degree, calculate the following measures (you must show all work to receive full credit):
a) What is the angle of elevation rounded to the nearest whole degree?
b) If the elevation of each step were changed to 10 inches and the landing became 7 inches,
what is the new angle of elevation for the staircase to the nearest whole degree?
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1 answer