Question

find ( mangle v ).
( mangle v=square^{circ} )

Explanation:

Step1: Recall the tangent function

In a right - triangle, \(\tan V=\frac{\text{opposite}}{\text{adjacent}}\). For \(\angle V\) in right - triangle \(TUV\), the side opposite to \(\angle V\) is \(UT = 6\), and the side adjacent to \(\angle V\) is \(TV=6\sqrt{3}\). So, \(\tan V=\frac{UT}{TV}\).

Step2: Substitute the values

Substitute \(UT = 6\) and \(TV = 6\sqrt{3}\) into the tangent formula: \(\tan V=\frac{6}{6\sqrt{3}}\). Simplify \(\frac{6}{6\sqrt{3}}=\frac{1}{\sqrt{3}}\).

Step3: Find the angle whose tangent is \(\frac{1}{\sqrt{3}}\)

We know that if \(\tan\theta=\frac{1}{\sqrt{3}}\), then \(\theta = 30^{\circ}\) (since \(\tan30^{\circ}=\frac{1}{\sqrt{3}}\)).

Answer:

\(30\)