Answer:
Height of vertical post relative to the horizontal is 6.3 ft
Height of vertical post above the roof (roofing sheets) is 4.0 ft
Step-by-step explanation:
Given the roof is 20° relative to the horizontal and the solar panel should be 38° relative to the horizontal, then finding the vertical support holding the back of the panel relative to the horizontal will be;
Apply the formula for sine of an angle as;
Sin of angle theta = opposite side length/hypotenuse
Sin 38° = O/8 where O is the length of opposite side of the angle
8*sin 38°=O
4.93 ft = O
Applying Pythagorean relationship to find the length from the bottom part of the panel to the vertical support relative to the horizontal will be;
a²+b²=c² where a=?, b=4.93 and c = 8
a²+4.93²=8²
a²=8²-4.93²
a=6.3 ft
Finding the height of the roof from the horizontal at 20° angle
Tan 20°= O/6.3
6.3 tan 20° = O
2.3 ft =O
Now finding the length of vertical post above the roof will be;
6.3-2.3=4.0 ft