Explain the difference between using the tangent ratio to solve for a missing angle in a right triangle versus using the cotangent ratio. You must use complete sentences and any evidence needed (such as an example) to prove your point of view. (10 points)

While determining the angle [tex]\theta[/tex] with the tangent ratio or cotangent ratio uses the same sides lengths but the ratios are inverse of each other.

Step-by-step explanation:

See the diagram attached.

Let us assume a right triangle Δ ABC with ∠ B = 90°. Now, assume that the angle ∠ CAB = [tex]\theta[/tex] and the sides AB, BC, CA are 3, 4, 5 units respectively.

The tangent ratio of an angle [tex]\theta[/tex] is given by

[tex]\tan \theta = \frac{BC}{AB} = \frac{4}{3}[/tex]

Again, the cotangent ratio of angle [tex]\theta[/tex] is given by

[tex]\cot \theta = \frac{AB}{BC} = \frac{3}{4}[/tex]

Therefore, in both the cases of tangent ratio and cotangent ratio are inverse of each other and while determining the angle [tex]\theta[/tex] with the tangent ratio or cotangent ratio uses the same sides lengths but the ratios are inverse of each other. (Answer)