The density of a certain material is such that it weighs 5 ounces per fluid ounce of volume. Express this density in pounds per
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Refer to the attached image. Since one vertex is the origin and the other two lay on the coordinate axes, the triangle is a right triangle. This means that, if we consider AB to the be base, AC is his height, and vice versa.
Anyway, it means that the area is given by
Since AB is a horizontal segment and AC is a vertical segment, their length is given by the absolute difference of the non-constant coordinate: points A and B share the same x coordinate, so we subtract the y coordinates:
The opposite goes for AC: points A and C share the same y coordinate, so we subtract the x coordinates:
So, the area is
As both and
determine terminal points in the fourth quadrant, we know that both angles fall between
and
. We also know that
for
, and that
is strictly increasing along this interval.
This means that the angle with the larger cosine value must be closer to having a measure of 360 degrees than the angle with the smaller cosine value, so .