Suppose the tangent of an acute angle in a right triangle is less than 1. How does the side opposite the angle compare to the side adjacent to the angle?
tangent of an angle is opposite/adjacent.
For angles >45°, the tangent > 1
for angles < 45°, the tangent < 1
so to get a value of < 1, the fraction must have been a proper fraction, that is, then opposite must have been less than the adjacent.
In a right triangle, the tangent of an acute angle is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle. If the tangent of an angle is less than 1, it means that the length of the side opposite the angle is shorter than the length of the side adjacent to the angle.
To determine how the side opposite the angle compares to the side adjacent to the angle, we can use the tangent function, which relates these two sides in a right triangle.
In a right triangle, the tangent of an acute angle is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle. Mathematically, it can be written as:
tan(angle) = opposite / adjacent
In this case, you mentioned that the tangent of the angle is less than 1. When the value of the tangent is less than 1, it means that the length of the side opposite the angle is smaller than the length of the side adjacent to the angle.
In simpler terms, if the tangent of an acute angle is less than 1, it indicates that the side opposite the angle is shorter than the side adjacent to the angle.