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

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:

1 answer

To find the sine ratio of angle Θ (angle C) in triangle ABC, we can use the definition of the sine function. The sine of an angle in a right triangle is the ratio of the length of the opposite side to the length of the hypotenuse.

In triangle ABC:

  • Angle A is the right angle.
  • The opposite side to angle C (side opposite to angle C) is side AB, which measures 12.
  • The hypotenuse is side BC, which measures 13.

Thus, the sine of angle C (Θ) can be calculated as follows:

\[ \sin(Θ) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{AB}{BC} = \frac{12}{13} \]

So, the sine ratio of angle Θ is:

Answer for Blank 1: 12/13