Question

find the exact value of sin q in simplest radical form.

Explanation:

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

In a right - triangle, \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). For \(\angle Q\), the side opposite to \(\angle Q\) is \(OP = 16\), and the hypotenuse is \(OQ=20\).

Step2: Calculate \(\sin Q\)

\(\sin Q=\frac{OP}{OQ}\)
Substitute \(OP = 16\) and \(OQ = 20\) into the formula: \(\sin Q=\frac{16}{20}\)
Simplify the fraction: \(\frac{16\div4}{20\div4}=\frac{4}{5}\)

Answer:

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