Find the tangent ratio of angle Θ. Clue: Use the slash symbol ( / ) to represent the fraction bar, and enter the fraction with no spaces.

Question

Triangle ABC is shown. AB measures 12. BC measures 13. CA measures 5. The angle formed at point C is marked theta, and angle A is the right angle.

Answer for Blank 1:

Answer 1

In triangle ABC, since angle A is the right angle, we can determine that:

• AB (the side opposite angle C, or Θ) = 12
• CA (the side adjacent to angle C, or Θ) = 5

The tangent ratio of angle Θ (or C) is defined as the ratio of the length of the opposite side to the length of the adjacent side. Therefore, the tangent ratio can be calculated as follows:

$\text{tan}(\Theta )=\frac{\text{opposite}}{\text{adjacent}}=\frac{AB}{CA}=\frac{12}{5}$.

Thus, the answer is:

12/5