Question

find ( mangle u ).
write your answer as an integer or as a decimal rounded to the nearest tenth.
( mangle u=) ( circ )

Explanation:

Step1: Recall the tangent function

In a right - triangle, \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). For \(\angle U\), the opposite side to \(\angle U\) is \(TV = 4\) and the adjacent side is \(TU=6\). So, \(\tan U=\frac{TV}{TU}\).

Step2: Substitute the values

Substitute \(TV = 4\) and \(TU = 6\) into the formula: \(\tan U=\frac{4}{6}=\frac{2}{3}\).

Step3: Find the angle

To find \(U\), use the inverse tangent function \(U=\tan^{- 1}(\frac{2}{3})\). Using a calculator, \(U=\tan^{-1}(\frac{2}{3})\approx33.7^{\circ}\).

Answer:

\(33.7^{\circ}\)