Question

find $m\angle q$.

write your answer as an integer or as a decimal rounded to the
e$m\angle q = \square^\circ$
submit

Explanation:

Step1: Identify triangle type and trigonometric ratio

We have a right - triangle \( \triangle QRS \) with \( \angle S = 90^{\circ} \), \( RS = 3 \) (opposite to \( \angle Q \)) and \( QS=6 \) (adjacent to \( \angle Q \)). We can use the tangent function, where \( \tan(\theta)=\frac{\text{opposite}}{\text{adjacent}} \). So for \( \angle Q \), \( \tan(\angle Q)=\frac{RS}{QS} \).

Step2: Calculate the tangent value

Substitute \( RS = 3 \) and \( QS = 6 \) into the formula: \( \tan(\angle Q)=\frac{3}{6}=\frac{1}{2} = 0.5 \).

Step3: Find the angle

To find \( \angle Q \), we take the arctangent (inverse tangent) of \( 0.5 \). Using a calculator, \( \angle Q=\arctan(0.5)\approx26.57^{\circ} \) (rounded to two decimal places) or if we round to the nearest whole number, it is \( 27^{\circ} \), but more accurately, \( \arctan(0.5)\approx26.57^{\circ} \)

Answer:

\( 26.6^{\circ} \) (or \( 26.57^{\circ} \), or \( 27^{\circ} \) depending on the required rounding. If rounded to one decimal place, it is \( 26.6^{\circ} \))