Question

find m∠s.
q 3.2 r
7.9
s
write your answer as an integer or as a decimal rounded to the nearest tenth.
m∠s = °

Explanation:

Step1: Identify triangle type and trigonometric ratio

This is a right - triangle \( \triangle QRS \) with \( \angle Q = 90^{\circ} \), \( QR = 3.2 \) (opposite to \( \angle S \)) and \( QS=7.9 \) (adjacent to \( \angle S \)). We can use the tangent function, where \( \tan(\theta)=\frac{\text{opposite}}{\text{adjacent}} \). So for \( \angle S \), \( \tan(\angle S)=\frac{QR}{QS}=\frac{3.2}{7.9} \).

Step2: Calculate the angle

First, calculate \( \frac{3.2}{7.9}\approx0.4051 \). Then, to find \( \angle S \), we take the arctangent (inverse tangent) of \( 0.4051 \). Using a calculator, \( \angle S=\arctan(0.4051) \). Calculating this, we get \( \angle S\approx22.0^{\circ} \) (rounded to the nearest tenth).

Answer:

\( 22.0 \)