Question

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

Explanation:

Step1: Recall the sine formula in a right - triangle

In a right - triangle, \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). For \(\angle T\), the side opposite to \(\angle T\) is \(UV = 2\), and the hypotenuse is \(VT=\sqrt{90}\).

Step2: Simplify the fraction

\(\sin T=\frac{UV}{VT}=\frac{2}{\sqrt{90}}\). Rationalize the denominator: \(\frac{2}{\sqrt{90}}=\frac{2}{\sqrt{9\times10}}=\frac{2}{3\sqrt{10}}=\frac{2\sqrt{10}}{3\times10}=\frac{\sqrt{10}}{15}\)

Answer:

\(\frac{\sqrt{10}}{15}\)