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?
Is it 15?
the angle is x, where
tan(x) = 2/(30*12)
Where did you get the 12?
You need to convert 30 feet to inches. That's where the 12 comes from.
To find the measure of the angle that the gutter makes with the roof, we need to use trigonometry.
Let's assume that the roof and the gutter form a right triangle, where the length of the gutter is the horizontal leg and the drop in height is the vertical leg. The angle between the roof and the gutter is the angle opposite the drop in height, which we need to find.
We can use the tangent function to calculate the angle. The tangent of an angle in a right triangle is defined as the ratio of the length of the opposite side to the adjacent side. In this case, the opposite side is the drop in height, and the adjacent side is the length of the gutter.
Given that the gutter drops 2 inches for every 30 feet of length, we can convert the measurements to the same unit. Using ratios, we can express this as 2 inches of drop for every 360 inches (30 feet) of length.
Now we have the ratio: opposite side (drop in height) = 2 inches, adjacent side (length of gutter) = 360 inches.
Using the tangent function, we can set up the equation: tan(angle) = opposite/adjacent.
tan(angle) = 2/360
To find the angle, we need to take the inverse tangent (arctan) of both sides of the equation.
angle = arctan(2/360)
Now, we can use a calculator to find the arctan of 2/360 and round it to the nearest tenth of a degree.
The approximate angle that the gutter makes with the roof is 0.33 degrees, which rounds to 0.3 degrees. Thus, the answer is not 15 degrees, but rather 0.3 degrees.