Question

look at the triangle:
what is the value of \\(\sin x^\circ\\)? (1 point)
\\(5 \div 13\\)
\\(12 \div 5\\)
\\(12 \div 13\\)
\\(5 \div 12\\)

Explanation:

Identify the given values

We examine the right-angled triangle:

• The hypotenuse is \(13\text{ cm}\).
• The side opposite to angle \(x^\circ\) is \(12\text{ cm}\).
• The side adjacent to angle \(x^\circ\) is \(5\text{ cm}\).

Apply the sine ratio

We use the definition of the sine function:

$$\sin(x^\circ) = \frac{\text{Opposite}}{\text{Hypotenuse}}$$

Calculate the value

We substitute the values into the formula:

$$\sin(x^\circ) = \frac{12}{13} = 12 \div 13$$

Answer:

• (A) \(5 \div 13\)
• (B) \(12 \div 5\)
• (C) \(12 \div 13\) (Correct answer)
• (D) \(5 \div 12\)