Sam is framing a closet under a stairway. The stairway is 17 ft 3 in. long, and its angle of elevation is 31degrees. Find the depth of the closet to the nearest inch.

Answer: the depth of the closet is 105.1 inches.

Step-by-step 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