Answer:
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.
[tex]13\text{ ft}+5\text{ inches}=((13\times 12)+5)\text{ inches}=161\text{ inches}[/tex]
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.
[tex]sin(34)=\frac{\text{Depth}}{161}[/tex]
[tex]\text{Depth}=161\cdot sin(34)[/tex]
[tex]\text{Depth}=161\cdot 0.559192903471[/tex]
[tex]\text{Depth}=90.030057458831 \approx 90[/tex]
Therefore, the depth of the closet to the nearest inch will be 90 inches.
Answer:
The depth of the closet is 90 inches.
Step-by-step explanation:
Given : Sam is framing a closet under a stairway. The stairway is 13 ft 5 in. long, and its angle of elevation is 34 degrees°.
To find : The depth of the closet to the nearest inch?
Solution :
According to question,
Firstly we form a right angle triangle ABC, forming an image of a closet under a stairway.
Refer the attached figure below.
The stairway is 13 ft 5 in. long i.e, the hypotenuse of the stairways.
AC= 13 ft. 5 in.
Conversion of feet into inches,
1 feet = 12 inches
13 feet = 13 × 12=156 inches
Total AC=156+5=161 inches.
Its angle of elevation is 34 degrees°.
i.e, [tex]\theta=\angle ACB=34^\circ[/tex]
We have to find the dept of the closet i.e, AB
Applying trigonometry property of right angle triangle,
[tex]\sin\theta=\frac{Perpendicular}{Hypotenuse}[/tex]
[tex]\sin\theta=\frac{AB}{AC}[/tex]
[tex]\sin(34)=\frac{AB}{161}[/tex]
[tex]AB=\sin(34)\times 161[/tex]
[tex]AB=0.559\times 161[/tex]
[tex]AB=90.03in.[/tex]
Therefore, The depth of the closet is 85 inches.
