In right triangle xyz, if angle $y$ is a right angle and the side opposite angle $x$ has length $5$, the side adjacent to angle $x$ has length $12$, and the hypotenuse has length $13$, what is $sinx$?

• A. $\frac{12}{5}$
• B. $\frac{5}{13}$
• C. $\frac{12}{13}$
• D. $\frac{5}{12}$

Answer: (B)

Verified step by step guidance

1. Identify the given information: triangle xyz is a right triangle with angle y as the right angle, the side opposite angle x has length 5, the side adjacent to angle x has length 12, and the hypotenuse has length 13.
2. Recall the definition of sine for an angle in a right triangle: \(\sin(x) = \frac{\text{opposite side to } x}{\text{hypotenuse}}\).
3. Using the given side lengths, substitute the opposite side length (5) and the hypotenuse length (13) into the sine formula: \(\sin(x) = \frac{5}{13}\).
4. Verify that the side lengths satisfy the Pythagorean theorem to confirm the triangle is valid: check if \$5^2 + 12^2 = 13^2$.
5. Conclude that \(\sin(x) = \frac{5}{13}\) is the correct expression for the sine of angle x based on the given triangle.