The area of the collector panel is (its length) x (its width).
You know the long dimension ... it's 12 feet.
You need to find the short dimension.
The short dimension is the hypotenuse of the right triangle at the end of
the whole setup ,,, the triangle colored black.
In that right triangle, the leg standing up is 5-ft, and the acute angle
that's down on the roof is 54° degrees. Can you find the length of
the hypotenuse with this much information ?
How about . . . . . sin(54°) = 5 / hypotenuse ?
(This is the big breakthrough. From here, the answer
practically falls into your lap.)
Multiply each side by 'hypotenuse' : sin(54°) x (hypotenuse) = 5
Divide each side by sin(54°) : Hypotenuse = 5 / sin(54°)
And there it is.
Area of the collector = (12-ft) x [ 5-ft / sin(54°) ]
That's (60 square feet) / sin(54°) = 74.164 square feet (rounded)
