Question

find ( mangle s ).

Explanation:

Step1: Use the tangent function

In a right - triangle, \(\tan S=\frac{opposite}{adjacent}\). Here, the opposite side to \(\angle S\) is \(UT = 5\sqrt{6}\), and the adjacent side to \(\angle S\) is \(TS=5\sqrt{6}\). So, \(\tan S=\frac{UT}{TS}\).
Substitute \(UT = 5\sqrt{6}\) and \(TS = 5\sqrt{6}\) into the formula: \(\tan S=\frac{5\sqrt{6}}{5\sqrt{6}} = 1\).

Step2: Find the angle whose tangent is 1

We know that if \(\tan\theta = 1\), then \(\theta=\arctan(1)\).
Since \(\tan45^{\circ}=1\), and \(S\) is an acute angle in a right - triangle (\(0^{\circ}

Answer:

\(45\)