Answer: the depth of the closet is 105.1 inches.
Explanation:
A right angle triangle is formed by the length of the stairway, its angle of elevation and the depth of the closet.
The length of the stairway represents the hypotenuse side of the right angle triangle. The depth, d of the closet represents the opposite side of the right angle triangle.
0.0833 feet = 1 inch
17 feet = 17/0.0833 = 204.1 inches
To determine d, we would apply
the Sine trigonometric ratio.
Sin θ, = opposite side/hypotenuse. Therefore,
Sin 31 = d/204.1
d = 204.1Sin31 = 204.1 × 0.515
d = 105.1 inches