Question

find ( mangle q ).
write your answer as an integer or as a decimal rounded to the nearest tenth.
( mangle q=square^{circ} )

Explanation:

Step1: Identify the trigonometric ratio

In right - triangle \(QSR\) with \(\angle S = 90^{\circ}\), we know the opposite side \(SR = 5.9\) and the adjacent side \(QS=5.4\) with respect to \(\angle Q\). We use the tangent ratio \( \tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). So, \(\tan Q=\frac{SR}{QS}\).

Step2: Substitute the values

Substitute \(SR = 5.9\) and \(QS = 5.4\) into the formula: \(\tan Q=\frac{5.9}{5.4}\approx1.0926\).

Step3: Find the angle

To find \(Q\), use the inverse tangent function \(Q=\tan^{- 1}(1.0926)\). Using a calculator, \(Q\approx47.5^{\circ}\).

Answer:

\(47.5\)