Question

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)

Answer 1

Answer:

While determining the angle $\theta$ 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 = $\theta$ and the sides AB, BC, CA are 3, 4, 5 units respectively.

The tangent ratio of an angle $\theta$ is given by  

$\tan \theta = \frac{BC}{AB} = \frac{4}{3}$  

Again, the cotangent ratio of angle $\theta$ is given by  

$\cot \theta = \frac{AB}{BC} = \frac{3}{4}$  

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