Question

find m∠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

We have a right triangle \( \triangle STU \) with \( \angle T = 90^\circ \), hypotenuse \( SU = 9.9 \), and opposite side to \( \angle S \) is \( TU = 7.1 \). We use the sine function: \( \sin(\angle S)=\frac{\text{opposite}}{\text{hypotenuse}}=\frac{TU}{SU} \).

Step2: Calculate the sine value

Substitute the values: \( \sin(\angle S)=\frac{7.1}{9.9}\approx0.7172 \).

Step3: Find the angle

Take the inverse sine: \( \angle S=\sin^{-1}(0.7172) \). Using a calculator, \( \angle S\approx45.8^\circ \) (rounded to the nearest tenth).

Answer:

\( 45.8 \)