A gutter at the edge of a roof drops 2 inches for every 30 feet of length. To the nearest tenth of a degree, what is the measure of the angle that the gutter makes with the roof?

I got an answer before, but where does 12 come from?

To find the angle that the gutter makes with the roof, we can use trigonometry. Specifically, we can use the tangent function.

The tangent of an angle is defined as the ratio of the length of the opposite side to the length of the adjacent side. In this case, the opposite side is the drop of the gutter (2 inches) and the adjacent side is the horizontal distance along the roof (30 feet).

Using the tangent function, we have:
tan(angle) = opposite / adjacent
tan(angle) = 2 inches / 30 feet

Now, we need to convert the units so that they are the same. We need to convert inches to feet. Since there are 12 inches in a foot, we divide 2 inches by 12 to get the value in feet:
2 inches / 12 = 1/6 feet

So now, we have:
tan(angle) = 1/6 feet / 30 feet

To find the angle, we can take the inverse tangent (also known as arctangent) of both sides:
angle = arctan(1/6 feet / 30 feet)

Using a calculator, we can evaluate this expression to find the angle. The result is approximately 0.2977 radians. To convert this to degrees, we multiply by 180 and divide by pi:
angle ≈ 0.2977 * 180 / pi ≈ 17.06 degrees

Therefore, to the nearest tenth of a degree, the measure of the angle that the gutter makes with the roof is approximately 17.1 degrees.

Regarding your question about the number 12, it comes from the fact that there are 12 inches in a foot. By dividing 2 inches by 12, we convert the units from inches to feet, which allows us to perform the trigonometric calculation correctly.