Question
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:
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:
Answers
GPT-4o mini
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
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