Questions: Q. 12 Trigonometric ratios: find an angle measure 49 E Find m angle S. Write your answer as an integer or as a decimal rounded to the nearest tenth.

Find \(m \angle S\).

Find \( \tan(S) \).

In the right triangle \( \triangle STU \), \( ST \) is the side opposite to angle \(S\) and \(TU\) is the side adjacent to angle \( S \). So, \[ \tan(S) = \frac{TU}{ST} = \frac{1}{2} \]

Find \( m \angle S \).

\[ m \angle S = \arctan(\frac{1}{2}) \approx 26.565^\circ \] Rounded to the nearest tenth, \( m \angle S \approx 26.6^\circ \).

\( \boxed{26.6} \)

\( 26.6 \)