Final answer:
The cosine ratio involves the side adjacent to the angle and the hypotenuse of a right triangle, while the secant ratio is the reciprocal of cosine, involving the hypotenuse over the adjacent side. An example with an adjacent side of 4 units and hypotenuse of 5 units would have a cosine value of 4/5 and a secant value of 5/4.
Step-by-step explanation:
The difference between using the cosine ratio and the secant ratio to solve for a missing angle in a right triangle is based on the sides of the triangle they each relate to. The cosine ratio involves the side adjacent to the angle and the hypotenuse. In contrast, the secant ratio is the reciprocal of the cosine ratio; it involves the hypotenuse over the adjacent side. Let's correct the options given:
- a. The cosine ratio involves adjacent and hypotenuse sides; secant ratio involves opposite and hypotenuse sides. (Incorrect)
- b. The cosine ratio involves opposite and adjacent sides; secant ratio involves adjacent and hypotenuse sides. (Incorrect)
- c. The cosine ratio involves opposite and hypotenuse sides; secant ratio involves adjacent and opposite sides. (Incorrect)
- d. The cosine ratio involves adjacent and hypotenuse sides; the secant ratio involves the hypotenuse and adjacent sides. (Correct)
For example, if we have a right triangle with an adjacent side (x) of 4 units and a hypotenuse (h) of 5 units, the cosine of the angle would be cos(θ) = x/h = 4/5. Conversely, the secant of the angle would be sec(θ) = h/x = 5/4.