Question

The staircase rises 52° from the ground and a vertical distance of 12 yards. How much horizontal distance does the staircase cover? Round to the nearest tenth.

Answer 1

For this case what we should do is use the following trigonometric formula.
tan (theta) = y / x
Where,
theta: angle
y: vertical distance
x: horizontal distance
Substituting values we have:
tan (52) = 12 / x
Clearing x:
x = (12) / (tan (52))
x = 9.375427518
Round to the nearest tenth:
x = 9.4 yards.
Answer:
the staircase covers:
x = 9.4 yards.