Sam is framing a closet under a stairway. the stairway is 13 ft 5 in. long, and its angle of elevation is 34 degrees°. find the depth of the closet to the nearest inch.

90 inches.

Step-by-step explanation:

Please find the attachment.

We have been given that Sam is framing a closet under a stairway. The length of the stairway is 13 ft 5 inch and its angle of elevation is 34 degrees°.

Let us convert length of staircase in inches.

We can see that closet under staircase is forming a right triangle with hypotenuse of 13 ft and 5 inches. The depth of the closet is opposite of 34 degrees angle.

Since we know that sine relates the hypotenuse and opposite side of a given angle (in a right triangle), therefore we will use sine to find the depth of closet.  

Therefore, the depth of the closet to the nearest inch will be 90 inches.  

convert the answer to millimeters there are 25.4 millimeters in an inch and 12 inches in a foot so just divide the 5280 feet into a fraction of the numbers till you get to the simplest form you need so (5280 x 12=63360 inches) (63360 x 25.4=1609344 millimeters) (5280/12=440 feet) its as simple as that just break it down to it's simplest form.