Question

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

Explanation:

Step1: Recall the definition of tangent

In a right triangle, the tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side. For angle \( V \) in right triangle \( \triangle VUT \) (with right angle at \( U \)), we need to identify the opposite and adjacent sides relative to \( V \).

Step2: Identify the sides

• Opposite side to \( V \): \( UT = 16 \) (since it is opposite angle \( V \))
• Adjacent side to \( V \): \( VU = 12 \) (since it is adjacent to angle \( V \) and not the hypotenuse)

Step3: Calculate \( \tan V \)

Using the definition of tangent, \( \tan V=\frac{\text{opposite}}{\text{adjacent}}=\frac{UT}{VU} \). Substituting the values, we get \( \tan V = \frac{16}{12} \). Simplifying this fraction by dividing numerator and denominator by their greatest common divisor (which is 4), we have \( \frac{16\div4}{12\div4}=\frac{4}{3} \).

Answer:

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