Answer:
Length of the roof line is [tex]17.4\ feet[/tex]. And depth of the shed is [tex]15.07\ feet[/tex]
Step-by-step explanation:
Given front wall is 11.5 feet tall, back wall is 20.2 feet. And roof rises at 30° angle from the front wall.
Let [tex]h[/tex] be the length of the roof line. And [tex]b[/tex] the depth of the shed.
We can see it is a right angle triangle with opposite [tex]20.2-11.5=8.7\ feet[/tex] (see the attachment)
Now,
[tex]sin(30)=\frac{Opposite}{Hypotenuse}\\ \\sin(30)=\frac{8.7}{h}\\\\h=\frac{8.7}{0.5}\\\\h=17.4\ feet[/tex]
Also,
[tex]tan(30)=\frac{Opposite}{Adjacent}\\\\tan(30)=\frac{8.7}{b}\\\\b=\frac{8.7}{tan(30)}\\\\b=\frac{8.7}{0.577}\\\\b=15.07\ feet[/tex]
So, Length of the roof line is [tex]17.4\ feet[/tex]. And depth of the shed is [tex]15.07\ feet[/tex]
Answer:
17.4 ft
Step-by-step explanation:
Given: Height of front wall is 11.5 ft
Height of back wall is 20.2 ft
Attach is the picture drawn for the question.
First lets find the depth of shed from from front to back wall.
Depth of shed from front to back wall= length of back wall - length of front wall.
∴ Depth of shed from front to back wall= [tex]20.2-11.5= 8.7\ ft[/tex]
Now, using sine rule of trignometry to find length of roof line.
We know, [tex]Sin \theta= \frac{Opposite}{Hypotenous}[/tex]
⇒ [tex]sin 30= \frac{8.7}{hypotenous}[/tex]
⇒ [tex]\frac{1}{2} = \frac{8.7}{Hypotenous}[/tex]
Cross multiplying
⇒ [tex]Hypontenous= 8.7\times 2[/tex]
∴ Hypontenous= 17.4 feet
Hence, length of roof line is 17.4 ft.
