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

Answer:

The depth is 127 inches.

Step-by-step 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 + $(\frac{6}{12} )$

               = 20.5 feet

So that applying the appropriate trigonometric function, we have;

Sin θ = $\frac{opposite}{hypotenuse}$

Sin 31º = $\frac{d}{20.5}$

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.