Question

find the sine of ∠x. simplify your answer and write it as a proper fraction, improper fraction, or whole number. sin(x) =

Explanation:

Step1: Recall sine definition

In a right triangle, \(\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}\). For \(\angle X\), opposite side is \(YZ = 16\), adjacent is \(XY = 12\). First, find hypotenuse \(XZ\) using Pythagorean theorem: \(a^2 + b^2 = c^2\), so \(XZ=\sqrt{12^2 + 16^2}=\sqrt{144 + 256}=\sqrt{400}=20\).

Step2: Calculate \(\sin(X)\)

Using \(\sin(X)=\frac{\text{opposite to }X}{\text{hypotenuse}}=\frac{YZ}{XZ}=\frac{16}{20}\). Simplify \(\frac{16}{20}\) by dividing numerator and denominator by 4: \(\frac{16\div4}{20\div4}=\frac{4}{5}\).

Answer:

\(\frac{4}{5}\)