Final answer:
The reference angle of a triangle is neither the hypotenuse, opposite, nor adjacent side; it is an angle. The Pythagorean theorem shows the relationship between the sides of a right triangle. The range of a projectile is zero at a launch angle of 90° or 0°.
Step-by-step explanation:
Understanding Right Triangles and Trigonometric Functions
When we look at right triangles, we are often interested in the relationships between the angles and the lengths of the sides. In the context of trigonometry, we use specific terms to refer to these sides based on the angle we are examining. The hypotenuse is the longest side of the right triangle, opposite the right angle, and is represented by the variable 'c' in the Pythagorean theorem. The Pythagorean theorem states that for a right triangle with legs labeled 'a' and 'b', and hypotenuse 'c', the relationship between the lengths of the sides is given by the equation a² + b² = c².
The side adjacent to a reference angle is simply called the adjacent side, and the side opposite the reference angle is known as the opposite side. In trigonometric functions, the cosine of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse (cos A = Ax/A), and the sine of an angle is the ratio of the length of the opposite side to the hypotenuse (sin A = Ay/A).
A common mistake is to assume that the reference angle is one of the sides of the triangle, but this is incorrect. The reference angle is an angle, not a side, so the correct answer to the given question about the reference angle is 'd) None of the above' since a reference angle is neither the hypotenuse, opposite, nor adjacent side.
In relation to projectile motion, the range of a projectile would be zero when its launch angle is vertical, meaning at 90° or when the object is not launched at all, at 0°. Therefore, the correct choice from the provided options is 'c. 90° or 0°'.