Ohio Assessments for Educators (OAE) Mathematics Practice Exam

What is the definition of tangent in a right triangle?

1. adj/hyp

2. hyp/adj

3. opp/adj

4. opp/hyp

The correct answer is: opp/adj

In the context of a right triangle, the tangent of an angle is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to that angle. Therefore, the correct definition of tangent corresponds to the relationship between these two sides in relation to the right angle. The terms used refer to the three sides of the triangle: the opposite side is the one opposite to the angle in question, the adjacent side is the one next to the angle that is not the hypotenuse, and the hypotenuse is the longest side of the triangle, located opposite the right angle. By understanding that tangent = opposite/adjacent, one can easily determine the value of the tangent for any given angle in a right triangle when the lengths of the relevant sides are known. This definition is crucial in various applications, including trigonometry, physics, and engineering, where analyzing angles and distances is fundamental.