The Laws of Sines Cosines Roof of a house

Question

The roof of a house is pitched at a 20◦ angle. An 8 foot solar panel is to be mounted on the roof and angled at 38◦ relative to the horizontal for maximum sun exposure, as shown in Figure 4. How long does the vertical support holding up the back of the panel need to be?

Answer 1

No figure submitted, but presumably the following suffices.

The solar panel forms a right triangle with altitude above horizontal of 8 sin 38 and base 8 cos 38.

The height of the roof above horizontal on the same line as the altitude of the solar panel is

8 cos 38 * tan 20.

The length of the support beam is the difference between these 2 numbers.