Ohio Assessments for Educators (OAE) Mathematics Practice Exam

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In right triangle trigonometry, what does the term "adjacent" refer to?

The side opposite the right angle
The side opposite the angle of interest
The side next to the angle of interest
The longest side of the triangle

The correct answer is: The side next to the angle of interest

In right triangle trigonometry, the term "adjacent" specifically refers to the side next to the angle of interest. In any right triangle, there are three sides: the hypotenuse, which is always the longest side and opposite the right angle, the opposite side, which is across from the angle of interest, and the adjacent side, which forms one of the two angles with the hypotenuse and is directly next to the angle in question. Understanding this concept is vital because it lays the foundation for using trigonometric ratios such as sine, cosine, and tangent, which relate these sides to the angles in the triangle. For example, cosine of an angle is defined as the ratio of the length of the adjacent side to the length of the hypotenuse. Recognizing the correct positioning of these sides in relation to the angle of interest helps in solving problems involving right triangles and their associated trigonometric functions.