The length of the roof line is equal to 17.4 feet and the depth of the shed is 15.07 feet.
Given the following data:
- Height of front wall = 11.5 feet.
- Height of back wall = 20.2 feet.
- Angle of inclination = 25°
How to calculate the length of the roofline.
First of all, we would assign a variable to the length of the roof line and depth of the shed from front to back respectively.
Let the length of the roof line be h.
Let the depth of the shed be d.
From the image attached, we would determine the length of the opposite side as follows:
[tex]Opp=20.2 -11.5[/tex]
Opposite side = 8.7 feet.
Next, we would determine the length of the roof line by using Sine trigonometric:
[tex]Sin \theta = \frac{Opp}{Hyp} \\\\Sin30 =\frac{8.7}{h} \\\\0.5=\frac{8.7}{h}\\\\h=\frac{8.7}{0.5}[/tex]
h = 17.4 feet.
For the depth;
We would determine the length of the roof line by using Tan trigonometric:
[tex]Tan \theta =\frac{Opp}{Adj} \\\\Tan 30 =\frac{8.7}{d} \\\\0.5774=\frac{8.7}{d}\\\\d=\frac{8.7}{0.5774}[/tex]
d = 15.07 feet.
Read more on trigonometry functions here: https://brainly.com/question/4515552
