Question

Sam is framing a closet under a stairway. The stairway is 20 ft 6 in. long, and its angle of elevation is 31º. Find the depth of the closet to the nearest inch.

Answer 1

The depth is 127 inches.

Explanation:

The stairway and its depth can be compared to a right angled triangle. Let the depth be represented by d.

But,

12 inches = 1 foot

20 ft 6 in = 20 +
`((6)/(12) )`

= 20.5 feet

So that applying the appropriate trigonometric function, we have;

Sin θ =
`(opposite)/(hypotenuse)`

Sin 31º =
`(d)/(20.5)`

d = 20.5 x Sin 31º

= 20.5 x 0.5150

d = 10.5575

d ≅ 11 feet

Therefore,

d = 10.5575 feet = (10.5575 x 12) inches

= 126.69 inches

The depth is 127 inches.