the roof of a house is at a 20 degree angle. an 8 foot solar panel is to be mounted on the roof, and should be angled 38 degrees relative to the horizontal for optimal results. how long does the vertical support holding up the back of the panel need to be?

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