Final Answer:
The tangent ratio of angle θ is given by a. tanθ = sinθ/cosθ (Option A).
Step-by-step explanation:
The tangent of an angle θ in a right-angled triangle is defined as the ratio of the length of the side opposite the angle (sinθ) to the length of the adjacent side (cosθ). Therefore, the correct expression for the tangent ratio is given by tanθ = sinθ/cosθ. This expression represents the fundamental definition of the tangent function in trigonometry (Option A).
To further understand this, consider a right-angled triangle where θ is one of the acute angles. The sine of θ (sinθ) is the ratio of the length of the side opposite θ to the hypotenuse, and the cosine of θ (cosθ) is the ratio of the length of the adjacent side to the hypotenuse. The tangent ratio (tanθ) is the ratio of sinθ to cosθ, capturing the relationship between the opposite and adjacent sides.
In conclusion, option a. tanθ = sinθ/cosθ accurately represents the tangent ratio of angle θ. This choice aligns with the fundamental definition of the tangent function, providing a clear and precise expression for the ratio of the lengths of the sides in a right-angled triangle.