Question

find the value of \\( \sin x \\) rounded to the nearest hundredth, if necessary.

triangle image with right angle at y, side yz = 12, side xz = 30

answer attempt 1 out of 2
\\( \sin x = \\) input box submit answer

Explanation:

Step1: Recall the definition of sine in a right - triangle

In a right - triangle, \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). For angle \(X\), the side opposite to angle \(X\) is \(YZ = 12\), and the hypotenuse is \(XZ=30\).

Step2: Calculate \(\sin X\)

Using the formula \(\sin X=\frac{YZ}{XZ}\), substitute \(YZ = 12\) and \(XZ = 30\) into the formula. So, \(\sin X=\frac{12}{30}\).
Simplify the fraction \(\frac{12}{30}=\frac{2}{5}=0.4\)

Answer:

\(0.4\)