In 25b3ABC, which ratio represents tan C?

Question

ScanSolve AI Tutor · Accepted Answer

Here are the solutions for questions 6 and 7:

6. In $\triangle ABC$ , which ratio represents $\tan A$ ?

In $\triangle ABC$ , with $\angle B = 90^\circ$ (as established in previous questions), the side opposite $\angle A$ is $BC$ and the side adjacent to $\angle A$ is $AB$ .
The tangent ratio is defined as $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$ .
Therefore, $\tan A = \frac{BC}{AB}$ .
Reviewing the given options, $\frac{BC}{AB}$ is not present.
Option c is $\frac{AB}{BC}$ , which represents $\tan C$ .
$\boxed{\text{c. } \frac{AB}{BC}}$

7. In $\triangle ABC$ , which ratio represents $\tan C$ ?
In $\triangle ABC$ , with $\angle B = 90^\circ$ , the side opposite $\angle C$ is $AB$ and the side adjacent to $\angle C$ is $BC$ .
The tangent ratio is defined as $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$ .
Therefore, $\tan C = \frac{AB}{BC}$ .
This ratio matches option c.
$\text{c. } \frac{AB}{BC}$

Answer