Question

find m∠s.
q
4.8
r
7.1
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 \( \angle R = 90^{\circ} \), \( QR = 4.8 \) (opposite to \( \angle S \)) and \( RS=7.1 \) (adjacent to \( \angle S \)). We can use the tangent function, where \( \tan(\theta)=\frac{\text{opposite}}{\text{adjacent}} \). So for \( \angle S \), \( \tan(\angle S)=\frac{QR}{RS}=\frac{4.8}{7.1} \)

Step2: Calculate the angle

First, calculate \( \frac{4.8}{7.1}\approx0.6761 \). Then, to find \( \angle S \), we take the arctangent (inverse tangent) of \( 0.6761 \). Using a calculator, \( \angle S=\arctan(0.6761) \). Calculating this, we get \( \angle S\approx34.1^{\circ} \) (rounded to the nearest tenth)

Answer:

\( 34.1 \)