Question

find the exact value of tan v in simplest radical form.

Explanation:

Step1: Recall the tangent ratio formula

In a right - triangle, \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). For angle \(V\), the side opposite to \(V\) is \(TU = 16\) and the side adjacent to \(V\) is \(VU=12\).

Step2: Calculate \(\tan V\)

Using the formula \(\tan V=\frac{TU}{VU}\), substitute \(TU = 16\) and \(VU = 12\). So, \(\tan V=\frac{16}{12}\). Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is \(4\). \(\frac{16\div4}{12\div4}=\frac{4}{3}\).

Answer:

\(\frac{4}{3}\)