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.

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.